LMFDB - Embedded newform 16.7.f.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,7,Mod(3,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68086533792$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	16.3
Dual form			16.7.f.a.11.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73714 + 7.80912i) q^{2} +(-8.66104 + 8.66104i) q^{3} +(-57.9647 + 27.1311i) q^{4} +(-38.1039 + 38.1039i) q^{5} +(-82.6805 - 52.5897i) q^{6} -108.944 q^{7} +(-312.563 - 405.523i) q^{8} +578.973i q^{9} +O(q^{10})$	\(q+(1.73714 + 7.80912i) q^{2} +(-8.66104 + 8.66104i) q^{3} +(-57.9647 + 27.1311i) q^{4} +(-38.1039 + 38.1039i) q^{5} +(-82.6805 - 52.5897i) q^{6} -108.944 q^{7} +(-312.563 - 405.523i) q^{8} +578.973i q^{9} +(-363.750 - 231.366i) q^{10} +(458.530 + 458.530i) q^{11} +(267.051 - 737.018i) q^{12} +(2298.86 + 2298.86i) q^{13} +(-189.251 - 850.759i) q^{14} -660.039i q^{15} +(2623.81 - 3145.29i) q^{16} +2457.77 q^{17} +(-4521.27 + 1005.76i) q^{18} +(1575.35 - 1575.35i) q^{19} +(1174.88 - 3242.48i) q^{20} +(943.571 - 943.571i) q^{21} +(-2784.18 + 4377.25i) q^{22} -17049.2 q^{23} +(6219.37 + 805.132i) q^{24} +12721.2i q^{25} +(-13958.7 + 21945.5i) q^{26} +(-11328.4 - 11328.4i) q^{27} +(6314.92 - 2955.77i) q^{28} +(4899.12 + 4899.12i) q^{29} +(5154.33 - 1146.58i) q^{30} -49584.6i q^{31} +(29119.9 + 15025.8i) q^{32} -7942.69 q^{33} +(4269.48 + 19193.0i) q^{34} +(4151.20 - 4151.20i) q^{35} +(-15708.1 - 33560.0i) q^{36} +(49011.4 - 49011.4i) q^{37} +(15038.7 + 9565.47i) q^{38} -39821.1 q^{39} +(27361.9 + 3542.15i) q^{40} +91183.4i q^{41} +(9007.57 + 5729.34i) q^{42} +(88105.2 + 88105.2i) q^{43} +(-39019.0 - 14138.1i) q^{44} +(-22061.1 - 22061.1i) q^{45} +(-29616.8 - 133139. i) q^{46} +39001.0i q^{47} +(4516.53 + 49966.4i) q^{48} -105780. q^{49} +(-99341.2 + 22098.5i) q^{50} +(-21286.8 + 21286.8i) q^{51} +(-195624. - 70882.3i) q^{52} +(73859.7 - 73859.7i) q^{53} +(68785.8 - 108144. i) q^{54} -34943.6 q^{55} +(34051.9 + 44179.4i) q^{56} +27288.3i q^{57} +(-29747.4 + 46768.3i) q^{58} +(264618. + 264618. i) q^{59} +(17907.6 + 38259.0i) q^{60} +(-119661. - 119661. i) q^{61} +(387212. - 86135.4i) q^{62} -63075.8i q^{63} +(-66753.4 + 253502. i) q^{64} -175191. q^{65} +(-13797.6 - 62025.5i) q^{66} +(182449. - 182449. i) q^{67} +(-142464. + 66681.8i) q^{68} +(147664. - 147664. i) q^{69} +(39628.5 + 25206.0i) q^{70} -224341. q^{71} +(234787. - 180965. i) q^{72} -172298. i q^{73} +(467876. + 297596. i) q^{74} +(-110179. - 110179. i) q^{75} +(-48573.6 + 134055. i) q^{76} +(-49954.2 - 49954.2i) q^{77} +(-69174.8 - 310968. i) q^{78} -219492. i q^{79} +(19870.3 + 219825. i) q^{80} -225840. q^{81} +(-712062. + 158398. i) q^{82} +(-207123. + 207123. i) q^{83} +(-29093.7 + 80293.9i) q^{84} +(-93650.5 + 93650.5i) q^{85} +(-534973. + 841075. i) q^{86} -84863.0 q^{87} +(42625.1 - 329264. i) q^{88} +463403. i q^{89} +(133955. - 210601. i) q^{90} +(-250448. - 250448. i) q^{91} +(988251. - 462563. i) q^{92} +(429454. + 429454. i) q^{93} +(-304563. + 67750.2i) q^{94} +120054. i q^{95} +(-382348. + 122069. i) q^{96} +1.45947e6 q^{97} +(-183755. - 826050. i) q^{98} +(-265476. + 265476. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) $ 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73714	+	7.80912i	0.217142	+	0.976140i
$2$	1.73714	+	7.80912i	0.217142	+	0.976140i
$3$	−8.66104	+	8.66104i	−0.320779	+	0.320779i	−0.849066	−	0.528287i	$-0.822835\pi$
$3$	−8.66104	+	8.66104i	−0.320779	+	0.320779i	0.528287	+	0.849066i	$0.322835\pi$
$4$	−57.9647	+	27.1311i	−0.905698	+	0.423923i
$5$	−38.1039	+	38.1039i	−0.304831	+	0.304831i	−0.842901	−	0.538069i	$-0.819154\pi$
$5$	−38.1039	+	38.1039i	−0.304831	+	0.304831i	0.538069	+	0.842901i	$0.319154\pi$
$6$	−82.6805	−	52.5897i	−0.382780	−	0.243471i
$7$	−108.944			−0.317622			−0.158811	−	0.987309i	$-0.550766\pi$
$7$	−108.944			−0.317622			−0.158811	+	0.987309i	$0.550766\pi$
$8$	−312.563	−	405.523i	−0.610474	−	0.792037i
$9$			578.973i			0.794201i
$10$	−363.750	−	231.366i	−0.363750	−	0.231366i
$11$	458.530	+	458.530i	0.344500	+	0.344500i	0.858056	−	0.513556i	$-0.171672\pi$
$11$	458.530	+	458.530i	0.344500	+	0.344500i	−0.513556	+	0.858056i	$0.671672\pi$
$12$	267.051	−	737.018i	0.154544	−	0.426515i
$13$	2298.86	+	2298.86i	1.04636	+	1.04636i	0.998872	+	0.0474934i	$0.0151233\pi$
$13$	2298.86	+	2298.86i	1.04636	+	1.04636i	0.0474934	+	0.998872i	$0.484877\pi$
$14$	−189.251	−	850.759i	−0.0689692	−	0.310043i
$15$		−	660.039i		−	0.195567i
$16$	2623.81	−	3145.29i	0.640579	−	0.767892i
$17$	2457.77			0.500258			0.250129	−	0.968213i	$-0.419527\pi$
$17$	2457.77			0.500258			0.250129	+	0.968213i	$0.419527\pi$
$18$	−4521.27	+	1005.76i	−0.775252	+	0.172455i
$19$	1575.35	−	1575.35i	0.229676	−	0.229676i	−0.582881	−	0.812557i	$-0.698075\pi$
$19$	1575.35	−	1575.35i	0.229676	−	0.229676i	0.812557	+	0.582881i	$0.198075\pi$
$20$	1174.88	−	3242.48i	0.146860	−	0.405310i
$21$	943.571	−	943.571i	0.101886	−	0.101886i
$22$	−2784.18	+	4377.25i	−0.261475	+	0.411086i
$23$	−17049.2			−1.40127			−0.700633	−	0.713522i	$-0.747099\pi$
$23$	−17049.2			−1.40127			−0.700633	+	0.713522i	$0.747099\pi$
$24$	6219.37	+	805.132i	0.449896	+	0.0582416i
$25$			12721.2i			0.814156i
$26$	−13958.7	+	21945.5i	−0.794188	+	1.24861i
$27$	−11328.4	−	11328.4i	−0.575543	−	0.575543i
$28$	6314.92	−	2955.77i	0.287669	−	0.134647i
$29$	4899.12	+	4899.12i	0.200874	+	0.200874i	0.800375	−	0.599500i	$-0.204634\pi$
$29$	4899.12	+	4899.12i	0.200874	+	0.200874i	−0.599500	+	0.800375i	$0.704634\pi$
$30$	5154.33	−	1146.58i	0.190901	−	0.0424660i
$31$		−	49584.6i		−	1.66442i	−0.554463	−	0.832208i	$-0.687076\pi$
$31$		−	49584.6i		−	1.66442i	0.554463	−	0.832208i	$-0.312924\pi$
$32$	29119.9	+	15025.8i	0.888667	+	0.458552i
$33$	−7942.69			−0.221017
$34$	4269.48	+	19193.0i	0.108627	+	0.488321i
$35$	4151.20	−	4151.20i	0.0968211	−	0.0968211i
$36$	−15708.1	−	33560.0i	−0.336680	−	0.719307i
$37$	49011.4	−	49011.4i	0.967592	−	0.967592i	−0.0318995	−	0.999491i	$-0.510156\pi$
$37$	49011.4	−	49011.4i	0.967592	−	0.967592i	0.999491	+	0.0318995i	$0.0101556\pi$
$38$	15038.7	+	9565.47i	0.274068	+	0.174323i
$39$	−39821.1			−0.671304
$40$	27361.9	+	3542.15i	0.427529	+	0.0553461i
$41$			91183.4i			1.32301i	0.749939	+	0.661507i	$0.230083\pi$
$41$			91183.4i			1.32301i	−0.749939	+	0.661507i	$0.769917\pi$
$42$	9007.57	+	5729.34i	0.121579	+	0.0773316i
$43$	88105.2	+	88105.2i	1.10814	+	1.10814i	0.993394	+	0.114750i	$0.0366066\pi$
$43$	88105.2	+	88105.2i	1.10814	+	1.10814i	0.114750	+	0.993394i	$0.463393\pi$
$44$	−39019.0	−	14138.1i	−0.458055	−	0.165972i
$45$	−22061.1	−	22061.1i	−0.242098	−	0.242098i
$46$	−29616.8	−	133139.i	−0.304274	−	1.36783i
$47$			39001.0i			0.375649i	0.982203	+	0.187824i	$0.0601436\pi$
$47$			39001.0i			0.375649i	−0.982203	+	0.187824i	$0.939856\pi$
$48$	4516.53	+	49966.4i	0.0408396	+	0.451808i
$49$	−105780.			−0.899116
$50$	−99341.2	+	22098.5i	−0.794730	+	0.176788i
$51$	−21286.8	+	21286.8i	−0.160472	+	0.160472i
$52$	−195624.	−	70882.3i	−1.39127	−	0.504113i
$53$	73859.7	−	73859.7i	0.496112	−	0.496112i	−0.414113	−	0.910225i	$-0.635908\pi$
$53$	73859.7	−	73859.7i	0.496112	−	0.496112i	0.910225	+	0.414113i	$0.135908\pi$
$54$	68785.8	−	108144.i	0.436835	−	0.686785i
$55$	−34943.6			−0.210029
$56$	34051.9	+	44179.4i	0.193900	+	0.251568i
$57$			27288.3i			0.147350i
$58$	−29747.4	+	46768.3i	−0.152463	+	0.239700i
$59$	264618.	+	264618.i	1.28844	+	1.28844i	0.935735	+	0.352704i	$0.114738\pi$
$59$	264618.	+	264618.i	1.28844	+	1.28844i	0.352704	+	0.935735i	$0.385262\pi$
$60$	17907.6	+	38259.0i	0.0829054	+	0.177125i
$61$	−119661.	−	119661.i	−0.527186	−	0.527186i	0.392547	−	0.919732i	$-0.371594\pi$
$61$	−119661.	−	119661.i	−0.527186	−	0.527186i	−0.919732	+	0.392547i	$0.871594\pi$
$62$	387212.	−	86135.4i	1.62470	−	0.361415i
$63$		−	63075.8i		−	0.252256i
$64$	−66753.4	+	253502.i	−0.254644	+	0.967035i
$65$	−175191.			−0.637930
$66$	−13797.6	−	62025.5i	−0.0479922	−	0.215744i
$67$	182449.	−	182449.i	0.606622	−	0.606622i	−0.335440	−	0.942062i	$-0.608885\pi$
$67$	182449.	−	182449.i	0.606622	−	0.606622i	0.942062	+	0.335440i	$0.108885\pi$
$68$	−142464.	+	66681.8i	−0.453082	+	0.212071i
$69$	147664.	−	147664.i	0.449497	−	0.449497i
$70$	39628.5	+	25206.0i	0.115535	+	0.0734870i
$71$	−224341.			−0.626807			−0.313404	−	0.949620i	$-0.601469\pi$
$71$	−224341.			−0.626807			−0.313404	+	0.949620i	$0.601469\pi$
$72$	234787.	−	180965.i	0.629036	−	0.484839i
$73$		−	172298.i		−	0.442907i	−0.975171	−	0.221453i	$-0.928920\pi$
$73$		−	172298.i		−	0.442907i	0.975171	−	0.221453i	$-0.0710801\pi$
$74$	467876.	+	297596.i	1.15461	+	0.734400i
$75$	−110179.	−	110179.i	−0.261164	−	0.261164i
$76$	−48573.6	+	134055.i	−0.110652	+	0.305382i
$77$	−49954.2	−	49954.2i	−0.109421	−	0.109421i
$78$	−69174.8	−	310968.i	−0.145769	−	0.655287i
$79$		−	219492.i		−	0.445181i	−0.974912	−	0.222591i	$-0.928549\pi$
$79$		−	219492.i		−	0.445181i	0.974912	−	0.222591i	$-0.0714514\pi$
$80$	19870.3	+	219825.i	0.0388092	+	0.429346i
$81$	−225840.			−0.424957
$82$	−712062.	+	158398.i	−1.29145	+	0.287282i
$83$	−207123.	+	207123.i	−0.362239	+	0.362239i	−0.864637	−	0.502398i	$-0.832451\pi$
$83$	−207123.	+	207123.i	−0.362239	+	0.362239i	0.502398	+	0.864637i	$0.332451\pi$
$84$	−29093.7	+	80293.9i	−0.0490864	+	0.135470i
$85$	−93650.5	+	93650.5i	−0.152494	+	0.152494i
$86$	−534973.	+	841075.i	−0.841078	+	1.32233i
$87$	−84863.0			−0.128873
$88$	42625.1	−	329264.i	0.0625485	−	0.483165i
$89$			463403.i			0.657338i	0.944445	+	0.328669i	$0.106600\pi$
$89$			463403.i			0.657338i	−0.944445	+	0.328669i	$0.893400\pi$
$90$	133955.	−	210601.i	0.183751	−	0.288891i
$91$	−250448.	−	250448.i	−0.332348	−	0.332348i
$92$	988251.	−	462563.i	1.26912	−	0.594029i
$93$	429454.	+	429454.i	0.533910	+	0.533910i
$94$	−304563.	+	67750.2i	−0.366686	+	0.0815693i
$95$			120054.i			0.140025i
$96$	−382348.	+	122069.i	−0.432160	+	0.137972i
$97$	1.45947e6			1.59911			0.799555	−	0.600592i	$-0.205068\pi$
$97$	1.45947e6			1.59911			0.799555	+	0.600592i	$0.205068\pi$
$98$	−183755.	−	826050.i	−0.195236	−	0.877663i
$99$	−265476.	+	265476.i	−0.273603	+	0.273603i
$100$	−345139.	−	737379.i	−0.345139	−	0.737379i
$101$	−393486.	+	393486.i	−0.381914	+	0.381914i	−0.871791	−	0.489877i	$-0.837042\pi$
$101$	−393486.	+	393486.i	−0.381914	+	0.381914i	0.489877	+	0.871791i	$0.337042\pi$
$102$	−203209.	−	129253.i	−0.191489	−	0.121798i
$103$	1.28496e6			1.17592			0.587959	−	0.808891i	$-0.299932\pi$
$103$	1.28496e6			1.17592			0.587959	+	0.808891i	$0.299932\pi$
$104$	213703.	−	1.65078e6i	0.189981	−	1.46754i
$105$			71907.5i			0.0621164i
$106$	705084.	+	448474.i	0.592002	+	0.376548i
$107$	−1.20045e6	−	1.20045e6i	−0.979923	−	0.979923i	0.0198794	−	0.999802i	$-0.493672\pi$
$107$	−1.20045e6	−	1.20045e6i	−0.979923	−	0.979923i	−0.999802	+	0.0198794i	$0.993672\pi$
$108$	963999.	+	349296.i	0.765254	+	0.277282i
$109$	818198.	+	818198.i	0.631799	+	0.631799i	0.948519	−	0.316720i	$-0.102582\pi$
$109$	818198.	+	818198.i	0.631799	+	0.631799i	−0.316720	+	0.948519i	$0.602582\pi$
$110$	−60701.9	−	272879.i	−0.0456062	−	0.205018i
$111$			848980.i			0.620767i
$112$	−285849.	+	342661.i	−0.203462	+	0.243899i
$113$	828433.			0.574146			0.287073	−	0.957909i	$-0.407318\pi$
$113$	828433.			0.574146			0.287073	+	0.957909i	$0.407318\pi$
$114$	−213097.	+	47403.6i	−0.143835	+	0.0319961i
$115$	649641.	−	649641.i	0.427150	−	0.427150i
$116$	−416895.	−	151058.i	−0.267087	−	0.0967763i
$117$	−1.33098e6	+	1.33098e6i	−0.831024	+	0.831024i
$118$	−1.60676e6	+	2.52612e6i	−0.977922	+	1.53747i
$119$	−267759.			−0.158893
$120$	−267661.	+	206304.i	−0.154896	+	0.119389i
$121$		−	1.35106e6i		−	0.762639i
$122$	726580.	−	1.14232e6i	0.400132	−	0.629081i
$123$	−789743.	−	789743.i	−0.424395	−	0.424395i
$124$	1.34528e6	+	2.87416e6i	0.705584	+	1.50746i
$125$	−1.08010e6	−	1.08010e6i	−0.553012	−	0.553012i
$126$	492566.	−	109571.i	0.246237	−	0.0547754i
$127$		−	302733.i		−	0.147791i	−0.997266	−	0.0738955i	$-0.976457\pi$
$127$		−	302733.i		−	0.147791i	0.997266	−	0.0738955i	$-0.0235431\pi$
$128$	−2.09559e6	−	80915.9i	−0.999255	−	0.0385837i
$129$	−1.52617e6			−0.710939
$130$	−304332.	−	1.36809e6i	−0.138522	−	0.622709i
$131$	−1.21146e6	+	1.21146e6i	−0.538883	+	0.538883i	−0.923201	−	0.384318i	$-0.874437\pi$
$131$	−1.21146e6	+	1.21146e6i	−0.538883	+	0.538883i	0.384318	+	0.923201i	$0.374437\pi$
$132$	460396.	−	215494.i	0.200175	−	0.0936942i
$133$	−171625.	+	171625.i	−0.0729500	+	0.0729500i
$134$	1.74171e6	+	1.10783e6i	0.723871	+	0.460425i
$135$	863314.			0.350887
$136$	−768205.	−	996680.i	−0.305394	−	0.396222i
$137$		−	4.75701e6i		−	1.85000i	−0.379963	−	0.925002i	$-0.624063\pi$
$137$		−	4.75701e6i		−	1.85000i	0.379963	−	0.925002i	$-0.375937\pi$
$138$	1.40964e6	+	896612.i	0.536377	+	0.341167i
$139$	680492.	+	680492.i	0.253384	+	0.253384i	0.822356	−	0.568973i	$-0.192659\pi$
$139$	680492.	+	680492.i	0.253384	+	0.253384i	−0.568973	+	0.822356i	$0.692659\pi$
$140$	−127997.	+	353250.i	−0.0466460	+	0.128735i
$141$	−337789.	−	337789.i	−0.120500	−	0.120500i
$142$	−389712.	−	1.75191e6i	−0.136106	−	0.611851i
$143$			2.10820e6i			0.720946i
$144$	1.82104e6	+	1.51911e6i	0.609861	+	0.508748i
$145$	−373352.			−0.122466
$146$	1.34550e6	−	299306.i	0.432339	−	0.0961739i
$147$	916166.	−	916166.i	0.288418	−	0.288418i
$148$	−1.51120e6	+	4.17066e6i	−0.466162	+	1.28653i
$149$	198695.	−	198695.i	0.0600660	−	0.0600660i	−0.676436	−	0.736502i	$-0.736476\pi$
$149$	198695.	−	198695.i	0.0600660	−	0.0600660i	0.736502	+	0.676436i	$0.236476\pi$
$150$	669003.	−	1.05179e6i	0.198223	−	0.311643i
$151$	3.65090e6			1.06040			0.530199	−	0.847874i	$-0.322117\pi$
$151$	3.65090e6			1.06040			0.530199	+	0.847874i	$0.322117\pi$
$152$	−1.13123e6	−	146445.i	−0.322123	−	0.0417006i
$153$			1.42298e6i			0.397305i
$154$	303321.	−	476876.i	0.0830501	−	0.130570i
$155$	1.88937e6	+	1.88937e6i	0.507366	+	0.507366i
$156$	2.30822e6	−	1.08039e6i	0.607999	−	0.284581i
$157$	−1.74133e6	−	1.74133e6i	−0.449969	−	0.449969i	0.445375	−	0.895344i	$-0.353070\pi$
$157$	−1.74133e6	−	1.74133e6i	−0.449969	−	0.449969i	−0.895344	+	0.445375i	$0.853070\pi$
$158$	1.71404e6	−	381288.i	0.434559	−	0.0966678i
$159$			1.27940e6i			0.318285i
$160$	−1.68212e6	+	537037.i	−0.410675	+	0.131113i
$161$	1.85741e6			0.445072
$162$	−392315.	−	1.76361e6i	−0.0922762	−	0.414817i
$163$	1.07659e6	−	1.07659e6i	0.248592	−	0.248592i	−0.571801	−	0.820393i	$-0.693755\pi$
$163$	1.07659e6	−	1.07659e6i	0.248592	−	0.248592i	0.820393	+	0.571801i	$0.193755\pi$
$164$	−2.47390e6	−	5.28542e6i	−0.560856	−	1.19825i
$165$	302648.	−	302648.i	0.0673730	−	0.0673730i
$166$	−1.97725e6	−	1.25765e6i	−0.432253	−	0.274938i
$167$	−4.73472e6			−1.01659			−0.508294	−	0.861184i	$-0.669724\pi$
$167$	−4.73472e6			−1.01659			−0.508294	+	0.861184i	$0.669724\pi$
$168$	−677564.	−	87714.5i	−0.142897	−	0.0184988i
$169$			5.74274e6i			1.18976i
$170$	−894012.	−	568644.i	−0.181969	−	0.115743i
$171$	912083.	+	912083.i	0.182409	+	0.182409i
$172$	−7.49738e6	−	2.71660e6i	−1.47341	−	0.533877i
$173$	2.22829e6	+	2.22829e6i	0.430362	+	0.430362i	0.888752	−	0.458389i	$-0.151573\pi$
$173$	2.22829e6	+	2.22829e6i	0.430362	+	0.430362i	−0.458389	+	0.888752i	$0.651573\pi$
$174$	−147419.	−	662705.i	−0.0279837	−	0.125798i
$175$		−	1.38590e6i		−	0.258594i
$176$	2.64530e6	−	239113.i	0.485219	−	0.0438596i
$177$	−4.58374e6			−0.826609
$178$	−3.61877e6	+	804995.i	−0.641654	+	0.142736i
$179$	−3.65587e6	+	3.65587e6i	−0.637429	+	0.637429i	−0.949921	−	0.312492i	$-0.898836\pi$
$179$	−3.65587e6	+	3.65587e6i	−0.637429	+	0.637429i	0.312492	+	0.949921i	$0.398836\pi$
$180$	1.87731e6	+	680225.i	0.321898	+	0.116637i
$181$	1.06804e6	−	1.06804e6i	0.180116	−	0.180116i	−0.611290	−	0.791406i	$-0.709349\pi$
$181$	1.06804e6	−	1.06804e6i	0.180116	−	0.180116i	0.791406	+	0.611290i	$0.209349\pi$
$182$	1.52072e6	−	2.39084e6i	0.252251	−	0.396585i
$183$	2.07278e6			0.338220
$184$	5.32894e6	+	6.91384e6i	0.855436	+	1.10985i
$185$			3.73506e6i			0.589905i
$186$	−2.60764e6	+	4.09968e6i	−0.405237	+	0.637106i
$187$	1.12696e6	+	1.12696e6i	0.172339	+	0.172339i
$188$	−1.05814e6	−	2.26068e6i	−0.159246	−	0.340224i
$189$	1.23416e6	+	1.23416e6i	0.182805	+	0.182805i
$190$	−937514.	+	208550.i	−0.136684	+	0.0304053i
$191$		−	6.72966e6i		−	0.965813i	−0.875672	−	0.482906i	$-0.839581\pi$
$191$		−	6.72966e6i		−	0.965813i	0.875672	−	0.482906i	$-0.160419\pi$
$192$	−1.61744e6	−	2.77375e6i	−0.228520	−	0.391889i
$193$	1.11685e6			0.155353			0.0776767	−	0.996979i	$-0.475250\pi$
$193$	1.11685e6			0.155353			0.0776767	+	0.996979i	$0.475250\pi$
$194$	2.53530e6	+	1.13971e7i	0.347235	+	1.56096i
$195$	1.51734e6	−	1.51734e6i	0.204635	−	0.204635i
$196$	6.13151e6	−	2.86993e6i	0.814328	−	0.381156i
$197$	8.99861e6	−	8.99861e6i	1.17700	−	1.17700i	0.196496	−	0.980505i	$-0.437044\pi$
$197$	8.99861e6	−	8.99861e6i	1.17700	−	1.17700i	0.980505	−	0.196496i	$-0.0629562\pi$
$198$	−2.53431e6	−	1.61197e6i	−0.326485	−	0.207664i
$199$	−1.35171e7			−1.71524			−0.857620	−	0.514283i	$-0.828058\pi$
$199$	−1.35171e7			−1.71524			−0.857620	+	0.514283i	$0.828058\pi$
$200$	5.15873e6	−	3.97616e6i	0.644841	−	0.497021i
$201$			3.16040e6i			0.389184i
$202$	−3.75632e6	−	2.38924e6i	−0.455731	−	0.289872i
$203$	−533731.	−	533731.i	−0.0638020	−	0.0638020i
$204$	656350.	−	1.81142e6i	0.0773116	−	0.213367i
$205$	−3.47445e6	−	3.47445e6i	−0.403296	−	0.403296i
$206$	2.23215e6	+	1.00344e7i	0.255342	+	1.14786i
$207$		−	9.87102e6i		−	1.11289i
$208$	1.32624e7	−	1.19880e6i	1.47377	−	0.133217i
$209$	1.44469e6			0.158247
$210$	−561534.	+	124913.i	−0.0606343	+	0.0134881i
$211$	8.88601e6	−	8.88601e6i	0.945931	−	0.945931i	−0.0526806	−	0.998611i	$-0.516777\pi$
$211$	8.88601e6	−	8.88601e6i	0.945931	−	0.945931i	0.998611	+	0.0526806i	$0.0167765\pi$
$212$	−2.27736e6	+	6.28514e6i	−0.239015	+	0.659641i
$213$	1.94303e6	−	1.94303e6i	0.201067	−	0.201067i
$214$	7.28909e6	−	1.14598e7i	0.743759	−	1.16932i
$215$	−6.71431e6			−0.675594
$216$	−1.05309e6	+	8.13476e6i	−0.104497	+	0.807204i
$217$			5.40196e6i			0.528655i
$218$	−4.96808e6	+	7.81073e6i	−0.479534	+	0.753914i
$219$	1.49228e6	+	1.49228e6i	0.142075	+	0.142075i
$220$	2.02549e6	−	948057.i	0.190223	−	0.0890361i
$221$	5.65007e6	+	5.65007e6i	0.523452	+	0.523452i
$222$	−6.62978e6	+	1.47480e6i	−0.605955	+	0.134795i
$223$		−	4.49427e6i		−	0.405270i	−0.979254	−	0.202635i	$-0.935049\pi$
$223$		−	4.49427e6i		−	0.405270i	0.979254	−	0.202635i	$-0.0649506\pi$
$224$	−3.17244e6	−	1.63698e6i	−0.282260	−	0.145646i
$225$	−7.36522e6			−0.646603
$226$	1.43910e6	+	6.46934e6i	0.124671	+	0.560447i
$227$	−1.13898e7	+	1.13898e7i	−0.973726	+	0.973726i	−0.999664	−	0.0259378i	$-0.991743\pi$
$227$	−1.13898e7	+	1.13898e7i	−0.973726	+	0.973726i	0.0259378	+	0.999664i	$0.491743\pi$
$228$	−740360.	−	1.58176e6i	−0.0624652	−	0.133455i
$229$	−8.61751e6	+	8.61751e6i	−0.717588	+	0.717588i	−0.968111	−	0.250523i	$-0.919398\pi$
$229$	−8.61751e6	+	8.61751e6i	−0.717588	+	0.717588i	0.250523	+	0.968111i	$0.419398\pi$
$230$	6.20165e6	+	3.94461e6i	0.509710	+	0.324206i
$231$	865311.			0.0701999
$232$	455424.	−	3.51799e6i	0.0364713	−	0.281728i
$233$		−	5.94391e6i		−	0.469899i	−0.972008	−	0.234949i	$-0.924508\pi$
$233$		−	5.94391e6i		−	0.469899i	0.972008	−	0.234949i	$-0.0754924\pi$
$234$	−1.27059e7	−	8.08168e6i	−0.991647	−	0.630745i
$235$	−1.48609e6	−	1.48609e6i	−0.114510	−	0.114510i
$236$	−2.25179e7	−	8.15914e6i	−1.71314	−	0.620738i
$237$	1.90103e6	+	1.90103e6i	0.142805	+	0.142805i
$238$	−465136.	−	2.09097e6i	−0.0345024	−	0.155102i
$239$			1.99463e7i			1.46106i	0.682881	+	0.730529i	$0.260727\pi$
$239$			1.99463e7i			1.46106i	−0.682881	+	0.730529i	$0.739273\pi$
$240$	−2.07601e6	−	1.73182e6i	−0.150175	−	0.125276i
$241$	−2.16169e6			−0.154434			−0.0772169	−	0.997014i	$-0.524603\pi$
$241$	−2.16169e6			−0.154434			−0.0772169	+	0.997014i	$0.524603\pi$
$242$	1.05506e7	−	2.34698e6i	0.744442	−	0.165601i
$243$	1.02144e7	−	1.02144e7i	0.711860	−	0.711860i
$244$	1.01827e7	+	3.68959e6i	0.700957	+	0.253985i
$245$	4.03064e6	−	4.03064e6i	0.274079	−	0.274079i
$246$	4.79531e6	−	7.53910e6i	0.322115	−	0.506424i
$247$	7.24301e6			0.480649
$248$	−2.01077e7	+	1.54983e7i	−1.31828	+	1.01608i
$249$		−	3.58781e6i		−	0.232397i
$250$	6.55835e6	−	1.03109e7i	0.419734	−	0.659899i
$251$	1.16373e7	+	1.16373e7i	0.735924	+	0.735924i	0.971786	−	0.235863i	$-0.0757916\pi$
$251$	1.16373e7	+	1.16373e7i	0.735924	+	0.735924i	−0.235863	+	0.971786i	$0.575792\pi$
$252$	1.71131e6	+	3.65617e6i	0.106937	+	0.228467i
$253$	−7.81757e6	−	7.81757e6i	−0.482737	−	0.482737i
$254$	2.36408e6	−	525889.i	0.144265	−	0.0320917i
$255$		−	1.62222e6i		−	0.0978340i
$256$	−3.00845e6	−	1.65053e7i	−0.179318	−	0.983791i
$257$	1.24535e7			0.733658			0.366829	−	0.930288i	$-0.380443\pi$
$257$	1.24535e7			0.733658			0.366829	+	0.930288i	$0.380443\pi$
$258$	−2.65116e6	−	1.19180e7i	−0.154375	−	0.693976i
$259$	−5.33951e6	+	5.33951e6i	−0.307328	+	0.307328i
$260$	1.01549e7	−	4.75313e6i	0.577772	−	0.270433i
$261$	−2.83646e6	+	2.83646e6i	−0.159535	+	0.159535i
$262$	−1.15649e7	−	7.35595e6i	−0.643040	−	0.409011i
$263$	2.05131e7			1.12762			0.563811	−	0.825904i	$-0.309335\pi$
$263$	2.05131e7			1.12762			0.563811	+	0.825904i	$0.309335\pi$
$264$	2.48259e6	+	3.22094e6i	0.134925	+	0.175054i
$265$			5.62869e6i			0.302461i
$266$	−1.63838e6	−	1.04210e6i	−0.0870500	−	0.0553689i
$267$	−4.01355e6	−	4.01355e6i	−0.210860	−	0.210860i
$268$	−5.62558e6	+	1.55257e7i	−0.292256	+	0.806578i
$269$	−5.10455e6	−	5.10455e6i	−0.262241	−	0.262241i	0.563723	−	0.825964i	$-0.309369\pi$
$269$	−5.10455e6	−	5.10455e6i	−0.262241	−	0.262241i	−0.825964	+	0.563723i	$0.809369\pi$
$270$	1.49970e6	+	6.74172e6i	0.0761925	+	0.342515i
$271$			2.60608e7i			1.30942i	0.755880	+	0.654711i	$0.227210\pi$
$271$			2.60608e7i			1.30942i	−0.755880	+	0.654711i	$0.772790\pi$
$272$	6.44871e6	−	7.73038e6i	0.320454	−	0.384144i
$273$	4.33828e6			0.213221
$274$	3.71481e7	−	8.26360e6i	1.80586	−	0.401714i
$275$	−5.83304e6	+	5.83304e6i	−0.280477	+	0.280477i
$276$	−4.55301e6	+	1.25656e7i	−0.216557	+	0.597661i
$277$	−1.28103e7	+	1.28103e7i	−0.602725	+	0.602725i	−0.941035	−	0.338310i	$-0.890145\pi$
$277$	−1.28103e7	+	1.28103e7i	−0.602725	+	0.602725i	0.338310	+	0.941035i	$0.390145\pi$
$278$	−4.13194e6	+	6.49616e6i	−0.192318	+	0.302358i
$279$	2.87081e7			1.32188
$280$	−2.98092e6	−	385897.i	−0.135793	−	0.0175791i
$281$		−	3.94268e7i		−	1.77694i	−0.458936	−	0.888469i	$-0.651769\pi$
$281$		−	3.94268e7i		−	1.77694i	0.458936	−	0.888469i	$-0.348231\pi$
$282$	2.05105e6	−	3.22462e6i	0.0914594	−	0.143791i
$283$	−2.18333e6	−	2.18333e6i	−0.0963298	−	0.0963298i	0.657300	−	0.753629i	$-0.271699\pi$
$283$	−2.18333e6	−	2.18333e6i	−0.0963298	−	0.0963298i	−0.753629	+	0.657300i	$0.771699\pi$
$284$	1.30039e7	−	6.08661e6i	0.567698	−	0.265718i
$285$	−1.03979e6	−	1.03979e6i	−0.0449171	−	0.0449171i
$286$	−1.64632e7	+	3.66223e6i	−0.703744	+	0.156548i
$287$		−	9.93391e6i		−	0.420218i
$288$	−8.69955e6	+	1.68596e7i	−0.364183	+	0.705781i
$289$	−1.80970e7			−0.749742
$290$	−648564.	−	2.91555e6i	−0.0265925	−	0.119544i
$291$	−1.26405e7	+	1.26405e7i	−0.512962	+	0.512962i
$292$	4.67464e6	+	9.98722e6i	0.187758	+	0.401140i
$293$	1.94896e6	−	1.94896e6i	0.0774819	−	0.0774819i	−0.667304	−	0.744786i	$-0.732552\pi$
$293$	1.94896e6	−	1.94896e6i	0.0774819	−	0.0774819i	0.744786	+	0.667304i	$0.232552\pi$
$294$	8.74596e6	+	5.56294e6i	0.344164	+	0.218908i
$295$	−2.01660e7			−0.785513
$296$	−3.51944e7	−	4.55611e6i	−1.35706	−	0.175679i
$297$		−	1.03888e7i		−	0.396549i
$298$	1.89680e6	+	1.20647e6i	0.0716757	+	0.0455899i
$299$	−3.91938e7	−	3.91938e7i	−1.46624	−	1.46624i
$300$	9.37574e6	+	3.39721e6i	0.347250	+	0.125823i
$301$	−9.59856e6	−	9.59856e6i	−0.351971	−	0.351971i
$302$	6.34212e6	+	2.85103e7i	0.230257	+	1.03510i
$303$		−	6.81601e6i		−	0.245020i
$304$	−821507.	−	9.08833e6i	−0.0292409	−	0.323492i
$305$	9.11912e6			0.321405
$306$	−1.11122e7	+	2.47191e6i	−0.387826	+	0.0862719i
$307$	1.85303e7	−	1.85303e7i	0.640424	−	0.640424i	−0.310235	−	0.950660i	$-0.600408\pi$
$307$	1.85303e7	−	1.85303e7i	0.640424	−	0.640424i	0.950660	+	0.310235i	$0.100408\pi$
$308$	4.25089e6	+	1.54027e6i	0.145488	+	0.0527163i
$309$	−1.11291e7	+	1.11291e7i	−0.377210	+	0.377210i
$310$	−1.14722e7	+	1.80364e7i	−0.385090	+	0.605431i
$311$	8.11836e6			0.269890			0.134945	−	0.990853i	$-0.456914\pi$
$311$	8.11836e6			0.269890			0.134945	+	0.990853i	$0.456914\pi$
$312$	1.24466e7	+	1.61484e7i	0.409814	+	0.531698i
$313$			1.24123e7i			0.404781i	0.979305	+	0.202390i	$0.0648709\pi$
$313$			1.24123e7i			0.404781i	−0.979305	+	0.202390i	$0.935129\pi$
$314$	1.05733e7	−	1.66232e7i	0.341526	−	0.536941i
$315$	2.40343e6	+	2.40343e6i	0.0768954	+	0.0768954i
$316$	5.95505e6	+	1.27228e7i	0.188723	+	0.403200i
$317$	1.88780e7	+	1.88780e7i	0.592623	+	0.592623i	0.938339	−	0.345716i	$-0.112364\pi$
$317$	1.88780e7	+	1.88780e7i	0.592623	+	0.592623i	−0.345716	+	0.938339i	$0.612364\pi$
$318$	−9.99101e6	+	2.22250e6i	−0.310691	+	0.0691132i
$319$			4.49279e6i			0.138403i
$320$	−7.11587e6	−	1.22030e7i	−0.217159	−	0.372406i
$321$	2.07943e7			0.628678
$322$	3.22658e6	+	1.45048e7i	0.0966441	+	0.434453i
$323$	3.87183e6	−	3.87183e6i	0.114897	−	0.114897i
$324$	1.30907e7	−	6.12727e6i	0.384883	−	0.180149i
$325$	−2.92443e7	+	2.92443e7i	−0.851904	+	0.851904i
$326$	1.02774e7	+	6.53702e6i	0.296640	+	0.188681i
$327$	−1.41729e7			−0.405336
$328$	3.69770e7	−	2.85005e7i	1.04788	−	0.807665i
$329$		−	4.24893e6i		−	0.119314i
$330$	2.88916e6	+	1.83767e6i	0.0803950	+	0.0511359i
$331$	−2.60503e7	−	2.60503e7i	−0.718339	−	0.718339i	0.249926	−	0.968265i	$-0.419594\pi$
$331$	−2.60503e7	−	2.60503e7i	−0.718339	−	0.718339i	−0.968265	+	0.249926i	$0.919594\pi$
$332$	6.38636e6	−	1.76253e7i	0.174518	−	0.481640i
$333$	2.83763e7	+	2.83763e7i	0.768463	+	0.768463i
$334$	−8.22487e6	−	3.69740e7i	−0.220744	−	0.992332i
$335$			1.39041e7i			0.369835i
$336$	−492050.	−	5.44355e6i	−0.0129715	−	0.143504i
$337$	6.04505e7			1.57946			0.789732	−	0.613452i	$-0.210219\pi$
$337$	6.04505e7			1.57946			0.789732	+	0.613452i	$0.210219\pi$
$338$	−4.48457e7	+	9.97594e6i	−1.16137	+	0.258347i
$339$	−7.17510e6	+	7.17510e6i	−0.184174	+	0.184174i
$340$	2.88759e6	−	7.96926e6i	0.0734680	−	0.202760i
$341$	2.27360e7	−	2.27360e7i	0.573392	−	0.573392i
$342$	−5.53815e6	+	8.70698e6i	−0.138448	+	0.217665i
$343$	2.43413e7			0.603201
$344$	8.19028e6	−	6.32670e7i	0.201198	−	1.55418i
$345$			1.12531e7i			0.274042i
$346$	−1.35302e7	+	2.12719e7i	−0.326644	+	0.513544i
$347$	3.18784e7	+	3.18784e7i	0.762971	+	0.762971i	0.976858	−	0.213888i	$-0.0686127\pi$
$347$	3.18784e7	+	3.18784e7i	0.762971	+	0.762971i	−0.213888	+	0.976858i	$0.568613\pi$
$348$	4.91906e6	−	2.30242e6i	0.116720	−	0.0546320i
$349$	1.29211e6	+	1.29211e6i	0.0303964	+	0.0303964i	0.722142	−	0.691745i	$-0.243158\pi$
$349$	1.29211e6	+	1.29211e6i	0.0303964	+	0.0303964i	−0.691745	+	0.722142i	$0.743158\pi$
$350$	1.08227e7	−	2.40750e6i	0.252423	−	0.0561516i
$351$		−	5.20849e7i		−	1.20446i
$352$	6.46253e6	+	2.02421e7i	0.148175	+	0.464118i
$353$	−3.28992e7			−0.747931			−0.373965	−	0.927443i	$-0.622002\pi$
$353$	−3.28992e7			−0.747931			−0.373965	+	0.927443i	$0.622002\pi$
$354$	−7.96260e6	−	3.57950e7i	−0.179492	−	0.806886i
$355$	8.54828e6	−	8.54828e6i	0.191070	−	0.191070i
$356$	−1.25726e7	−	2.68610e7i	−0.278660	−	0.595350i
$357$	2.31908e6	−	2.31908e6i	0.0509695	−	0.0509695i
$358$	−3.48999e7	−	2.21984e7i	−0.760633	−	0.483807i
$359$	−6.77438e7			−1.46415			−0.732076	−	0.681223i	$-0.761448\pi$
$359$	−6.77438e7			−1.46415			−0.732076	+	0.681223i	$0.761448\pi$
$360$	−2.05081e6	+	1.58418e7i	−0.0439559	+	0.339544i
$361$			4.20824e7i			0.894498i
$362$	1.01958e7	+	6.48512e6i	0.214929	+	0.136708i
$363$	1.17016e7	+	1.17016e7i	0.244639	+	0.244639i
$364$	2.13121e7	+	7.72222e6i	0.441897	+	0.160117i
$365$	6.56524e6	+	6.56524e6i	0.135012	+	0.135012i
$366$	3.60071e6	+	1.61866e7i	0.0734420	+	0.330150i
$367$			7.23881e7i			1.46443i	0.681073	+	0.732216i	$0.261514\pi$
$367$			7.23881e7i			1.46443i	−0.681073	+	0.732216i	$0.738486\pi$
$368$	−4.47339e7	+	5.36246e7i	−0.897621	+	1.07602i
$369$	−5.27927e7			−1.05074
$370$	−2.91675e7	+	6.48831e6i	−0.575830	+	0.128093i
$371$	−8.04659e6	+	8.04659e6i	−0.157576	+	0.157576i
$372$	−3.65448e7	−	1.32416e7i	−0.709898	−	0.257225i
$373$	3.20249e7	−	3.20249e7i	0.617108	−	0.617108i	−0.327681	−	0.944789i	$-0.606267\pi$
$373$	3.20249e7	−	3.20249e7i	0.617108	−	0.617108i	0.944789	+	0.327681i	$0.106267\pi$
$374$	−6.84287e6	+	1.07582e7i	−0.130805	+	0.205649i
$375$	1.87096e7			0.354789
$376$	1.58158e7	−	1.21902e7i	0.297528	−	0.229324i
$377$			2.25248e7i			0.420376i
$378$	−7.49382e6	+	1.17817e7i	−0.138748	+	0.218138i
$379$	1.95700e7	+	1.95700e7i	0.359479	+	0.359479i	0.863621	−	0.504142i	$-0.168191\pi$
$379$	1.95700e7	+	1.95700e7i	0.359479	+	0.359479i	−0.504142	+	0.863621i	$0.668191\pi$
$380$	−3.25719e6	−	6.95888e6i	−0.0593597	−	0.126820i
$381$	2.62198e6	+	2.62198e6i	0.0474083	+	0.0474083i
$382$	5.25527e7	−	1.16904e7i	0.942768	−	0.209719i
$383$		−	9.29760e7i		−	1.65491i	−0.561531	−	0.827456i	$-0.689787\pi$
$383$		−	9.29760e7i		−	1.65491i	0.561531	−	0.827456i	$-0.310213\pi$
$384$	1.88508e7	−	1.74492e7i	0.332917	−	0.308164i
$385$	3.80690e6			0.0667098
$386$	1.94012e6	+	8.72158e6i	0.0337338	+	0.151647i
$387$	−5.10105e7	+	5.10105e7i	−0.880089	+	0.880089i
$388$	−8.45975e7	+	3.95969e7i	−1.44831	+	0.677900i
$389$	1.13266e7	−	1.13266e7i	0.192420	−	0.192420i	−0.604321	−	0.796741i	$-0.706555\pi$
$389$	1.13266e7	−	1.13266e7i	0.192420	−	0.192420i	0.796741	+	0.604321i	$0.206555\pi$
$390$	1.44849e7	+	9.21326e6i	0.244187	+	0.155317i
$391$	−4.19029e7			−0.700994
$392$	3.30629e7	+	4.28963e7i	0.548887	+	0.712133i
$393$		−	2.09850e7i		−	0.345725i
$394$	8.59030e7	+	5.46394e7i	1.40449	+	0.893340i
$395$	8.36350e6	+	8.36350e6i	0.135705	+	0.135705i
$396$	8.18560e6	−	2.25909e7i	0.131815	−	0.363788i
$397$	−7.57489e7	−	7.57489e7i	−1.21061	−	1.21061i	−0.970826	−	0.239785i	$-0.922923\pi$
$397$	−7.57489e7	−	7.57489e7i	−1.21061	−	1.21061i	−0.239785	−	0.970826i	$-0.577077\pi$
$398$	−2.34811e7	−	1.05557e8i	−0.372452	−	1.67431i
$399$		−	2.97290e6i		−	0.0468017i
$400$	4.00118e7	+	3.33780e7i	0.625184	+	0.521531i
$401$	−6.10535e7			−0.946841			−0.473421	−	0.880836i	$-0.656981\pi$
$401$	−6.10535e7			−0.946841			−0.473421	+	0.880836i	$0.656981\pi$
$402$	−2.46800e7	+	5.49006e6i	−0.379898	+	0.0845083i
$403$	1.13988e8	−	1.13988e8i	1.74159	−	1.74159i
$404$	1.21326e7	−	3.34840e7i	0.183997	−	0.507801i
$405$	8.60537e6	−	8.60537e6i	0.129540	−	0.129540i
$406$	3.24081e6	−	5.09514e6i	0.0484256	−	0.0761338i
$407$	4.49464e7			0.666671
$408$	1.52857e7	+	1.97883e6i	0.225064	+	0.0291358i
$409$			1.51063e7i			0.220795i	0.993888	+	0.110397i	$0.0352124\pi$
$409$			1.51063e7i			0.220795i	−0.993888	+	0.110397i	$0.964788\pi$
$410$	2.10968e7	−	3.31680e7i	0.306101	−	0.481246i
$411$	4.12007e7	+	4.12007e7i	0.593443	+	0.593443i
$412$	−7.44821e7	+	3.48622e7i	−1.06503	+	0.498498i
$413$	−2.88286e7	−	2.88286e7i	−0.409236	−	0.409236i
$414$	7.70840e7	−	1.71473e7i	1.08633	−	0.241655i
$415$		−	1.57844e7i		−	0.220843i
$416$	3.24002e7	+	1.01485e8i	0.450057	+	1.40968i
$417$	−1.17875e7			−0.162561
$418$	2.50962e6	+	1.12817e7i	0.0343621	+	0.154471i
$419$	−4.98380e7	+	4.98380e7i	−0.677515	+	0.677515i	−0.959437	−	0.281922i	$-0.909028\pi$
$419$	−4.98380e7	+	4.98380e7i	−0.677515	+	0.677515i	0.281922	+	0.959437i	$0.409028\pi$
$420$	−1.95093e6	−	4.16810e6i	−0.0263326	−	0.0562587i
$421$	8.59072e7	−	8.59072e7i	1.15129	−	1.15129i	0.164991	−	0.986295i	$-0.447240\pi$
$421$	8.59072e7	−	8.59072e7i	1.15129	−	1.15129i	0.986295	−	0.164991i	$-0.0527597\pi$
$422$	8.48281e7	+	5.39557e7i	1.12876	+	0.717959i
$423$	−2.25805e7			−0.298341
$424$	−5.30375e7	−	6.86601e6i	−0.695802	−	0.0900756i
$425$			3.12657e7i			0.407288i
$426$	1.85486e7	+	1.17980e7i	0.239929	+	0.152609i
$427$	1.30364e7	+	1.30364e7i	0.167446	+	0.167446i
$428$	1.02153e8	+	3.70142e7i	1.30293	+	0.472103i
$429$	−1.82592e7	−	1.82592e7i	−0.231265	−	0.231265i
$430$	−1.16637e7	−	5.24328e7i	−0.146700	−	0.659475i
$431$			5.19997e7i			0.649484i	0.945803	+	0.324742i	$0.105278\pi$
$431$			5.19997e7i			0.649484i	−0.945803	+	0.324742i	$0.894722\pi$
$432$	−6.53547e7	+	5.90750e6i	−0.810635	+	0.0732745i
$433$	2.45395e7			0.302275			0.151138	−	0.988513i	$-0.451706\pi$
$433$	2.45395e7			0.302275			0.151138	+	0.988513i	$0.451706\pi$
$434$	−4.21845e7	+	9.38396e6i	−0.516041	+	0.114793i
$435$	3.23361e6	−	3.23361e6i	0.0392844	−	0.0392844i
$436$	−6.96251e7	−	2.52280e7i	−0.840053	−	0.304385i
$437$	−2.68584e7	+	2.68584e7i	−0.321837	+	0.321837i
$438$	−9.06111e6	+	1.42457e7i	−0.107835	+	0.169536i
$439$	−3.41967e7			−0.404195			−0.202097	−	0.979365i	$-0.564776\pi$
$439$	−3.41967e7			−0.404195			−0.202097	+	0.979365i	$0.564776\pi$
$440$	1.09221e7	+	1.41704e7i	0.128217	+	0.166351i
$441$		−	6.12438e7i		−	0.714079i
$442$	−3.43071e7	+	5.39370e7i	−0.397299	+	0.624626i
$443$	6.31270e7	+	6.31270e7i	0.726113	+	0.726113i	0.969843	−	0.243730i	$-0.0783711\pi$
$443$	6.31270e7	+	6.31270e7i	0.726113	+	0.726113i	−0.243730	+	0.969843i	$0.578371\pi$
$444$	−2.30337e7	−	4.92109e7i	−0.263157	−	0.562227i
$445$	−1.76575e7	−	1.76575e7i	−0.200377	−	0.200377i
$446$	3.50963e7	−	7.80718e6i	0.395601	−	0.0880014i
$447$			3.44181e6i			0.0385358i
$448$	7.27240e6	−	2.76176e7i	0.0808804	−	0.307151i
$449$	−8.08164e7			−0.892813			−0.446407	−	0.894830i	$-0.647297\pi$
$449$	−8.08164e7			−0.892813			−0.446407	+	0.894830i	$0.647297\pi$
$450$	−1.27944e7	−	5.75159e7i	−0.140405	−	0.631175i
$451$	−4.18103e7	+	4.18103e7i	−0.455779	+	0.455779i
$452$	−4.80199e7	+	2.24763e7i	−0.520003	+	0.243394i
$453$	−3.16206e7	+	3.16206e7i	−0.340153	+	0.340153i
$454$	−1.08730e8	−	6.91583e7i	−1.16193	−	0.739055i
$455$	1.90861e7			0.202620
$456$	1.10660e7	−	8.52929e6i	0.116707	−	0.0899536i
$457$		−	6.62724e6i		−	0.0694359i	−0.999397	−	0.0347180i	$-0.988947\pi$
$457$		−	6.62724e6i		−	0.0694359i	0.999397	−	0.0347180i	$-0.0110533\pi$
$458$	−8.22650e7	−	5.23253e7i	−0.856285	−	0.544648i
$459$	−2.78426e7	−	2.78426e7i	−0.287920	−	0.287920i
$460$	−2.00308e7	+	5.52817e7i	−0.205790	+	0.567947i
$461$	1.09225e8	+	1.09225e8i	1.11486	+	1.11486i	0.992484	+	0.122373i	$0.0390503\pi$
$461$	1.09225e8	+	1.09225e8i	1.11486	+	1.11486i	0.122373	+	0.992484i	$0.460950\pi$
$462$	1.50317e6	+	6.75732e6i	0.0152434	+	0.0685249i
$463$			2.76673e7i			0.278756i	0.990239	+	0.139378i	$0.0445103\pi$
$463$			2.76673e7i			0.278756i	−0.990239	+	0.139378i	$0.955490\pi$
$464$	2.82635e7	−	2.55478e6i	0.282926	−	0.0255740i
$465$	−3.27278e7			−0.325505
$466$	4.64167e7	−	1.03254e7i	0.458687	−	0.102035i
$467$	3.09232e7	−	3.09232e7i	0.303622	−	0.303622i	−0.538807	−	0.842429i	$-0.681125\pi$
$467$	3.09232e7	−	3.09232e7i	0.303622	−	0.303622i	0.842429	+	0.538807i	$0.181125\pi$
$468$	4.10389e7	−	1.13261e8i	0.400367	−	1.10495i
$469$	−1.98768e7	+	1.98768e7i	−0.192676	+	0.192676i
$470$	9.02351e6	−	1.41866e7i	0.0869124	−	0.136642i
$471$	3.01635e7			0.288682
$472$	2.45990e7	−	1.90019e8i	0.233933	−	1.80705i
$473$			8.07978e7i			0.763512i
$474$	−1.15430e7	+	1.81477e7i	−0.108389	+	0.170407i
$475$	2.00403e7	+	2.00403e7i	0.186992	+	0.186992i
$476$	1.55206e7	−	7.26460e6i	0.143909	−	0.0673583i
$477$	4.27627e7	+	4.27627e7i	0.394013	+	0.394013i
$478$	−1.55763e8	+	3.46494e7i	−1.42620	+	0.317258i
$479$		−	2.32071e7i		−	0.211161i	−0.994411	−	0.105580i	$-0.966330\pi$
$479$		−	2.32071e7i		−	0.211161i	0.994411	−	0.105580i	$-0.0336701\pi$
$480$	9.91765e6	−	1.92202e7i	0.0896778	−	0.173794i
$481$	2.25341e8			2.02491
$482$	−3.75516e6	−	1.68809e7i	−0.0335341	−	0.150749i
$483$	−1.60871e7	+	1.60871e7i	−0.142770	+	0.142770i
$484$	3.66557e7	+	7.83139e7i	0.323300	+	0.690721i
$485$	−5.56114e7	+	5.56114e7i	−0.487459	+	0.487459i
$486$	9.75094e7	+	6.20217e7i	0.849450	+	0.540300i
$487$	−1.54147e8			−1.33459			−0.667297	−	0.744792i	$-0.732549\pi$
$487$	−1.54147e8			−1.33459			−0.667297	+	0.744792i	$0.732549\pi$
$488$	−1.11237e7	+	8.59269e7i	−0.0957174	+	0.739383i
$489$			1.86488e7i			0.159486i
$490$	3.84775e7	+	2.44740e7i	0.327054	+	0.208025i
$491$	−1.14203e8	−	1.14203e8i	−0.964788	−	0.964788i	0.0346133	−	0.999401i	$-0.488980\pi$
$491$	−1.14203e8	−	1.14203e8i	−0.964788	−	0.964788i	−0.999401	+	0.0346133i	$0.988980\pi$
$492$	6.72038e7	+	2.43507e7i	0.564285	+	0.204463i
$493$	1.20409e7	+	1.20409e7i	0.100489	+	0.100489i
$494$	1.25821e7	+	5.65616e7i	0.104369	+	0.469181i
$495$		−	2.02314e7i		−	0.166805i
$496$	−1.55958e8	−	1.30101e8i	−1.27809	−	1.06619i
$497$	2.44407e7			0.199088
$498$	2.80176e7	−	6.23252e6i	0.226852	−	0.0504633i
$499$	1.08426e8	−	1.08426e8i	0.872637	−	0.872637i	−0.120122	−	0.992759i	$-0.538329\pi$
$499$	1.08426e8	−	1.08426e8i	0.872637	−	0.872637i	0.992759	+	0.120122i	$0.0383287\pi$
$500$	9.19120e7	+	3.33034e7i	0.735296	+	0.266427i
$501$	4.10076e7	−	4.10076e7i	0.326100	−	0.326100i
$502$	−7.06617e7	+	1.11093e8i	−0.558564	+	0.878165i
$503$	2.09927e8			1.64955			0.824774	−	0.565462i	$-0.191302\pi$
$503$	2.09927e8			1.64955			0.824774	+	0.565462i	$0.191302\pi$
$504$	−2.55787e7	+	1.97151e7i	−0.199796	+	0.153995i
$505$		−	2.99868e7i		−	0.232839i
$506$	4.74681e7	−	7.46285e7i	0.366396	−	0.576041i
$507$	−4.97381e7	−	4.97381e7i	−0.381650	−	0.381650i
$508$	8.21346e6	+	1.75478e7i	0.0626520	+	0.133854i
$509$	3.46663e7	+	3.46663e7i	0.262878	+	0.262878i	0.826222	−	0.563344i	$-0.190485\pi$
$509$	3.46663e7	+	3.46663e7i	0.262878	+	0.262878i	−0.563344	+	0.826222i	$0.690485\pi$
$510$	1.26681e7	−	2.81803e6i	0.0954997	−	0.0212439i
$511$			1.87709e7i			0.140677i
$512$	1.23666e8	−	5.21653e7i	0.921380	−	0.388662i
$513$	−3.56923e7			−0.264376
$514$	2.16336e7	+	9.72512e7i	0.159308	+	0.716153i
$515$	−4.89619e7	+	4.89619e7i	−0.358457	+	0.358457i
$516$	8.84637e7	−	4.14065e7i	0.643897	−	0.301383i
$517$	−1.78831e7	+	1.78831e7i	−0.129411	+	0.129411i
$518$	−5.09724e7	−	3.24214e7i	−0.366729	−	0.233261i
$519$	−3.85987e7			−0.276103
$520$	5.47583e7	+	7.10441e7i	0.389439	+	0.505264i
$521$		−	1.53422e8i		−	1.08486i	−0.840100	−	0.542432i	$-0.817504\pi$
$521$		−	1.53422e8i		−	1.08486i	0.840100	−	0.542432i	$-0.182496\pi$
$522$	−2.70776e7	−	1.72229e7i	−0.190370	−	0.121086i
$523$	−1.85766e8	−	1.85766e8i	−1.29856	−	1.29856i	−0.929343	−	0.369217i	$-0.879626\pi$
$523$	−1.85766e8	−	1.85766e8i	−1.29856	−	1.29856i	−0.369217	−	0.929343i	$-0.620374\pi$
$524$	3.73536e7	−	1.03090e8i	0.259621	−	0.716510i
$525$	1.20033e7	+	1.20033e7i	0.0829514	+	0.0829514i
$526$	3.56341e7	+	1.60189e8i	0.244855	+	1.10072i
$527$		−	1.21867e8i		−	0.832637i
$528$	−2.08401e7	+	2.49821e7i	−0.141579	+	0.169717i
$529$	1.42639e8			0.963545
$530$	−4.39551e7	+	9.77782e6i	−0.295244	+	0.0656771i
$531$	−1.53207e8	+	1.53207e8i	−1.02328	+	1.02328i
$532$	5.29182e6	−	1.46046e7i	0.0351455	−	0.0969959i
$533$	−2.09618e8	+	2.09618e8i	−1.38436	+	1.38436i
$534$	2.43702e7	−	3.83144e7i	0.160042	−	0.251616i
$535$	9.14836e7			0.597423
$536$	−1.31014e8	−	1.69605e7i	−0.850794	−	0.110140i
$537$		−	6.33273e7i		−	0.408948i
$538$	3.09947e7	−	4.87293e7i	0.199040	−	0.312927i
$539$	−4.85034e7	−	4.85034e7i	−0.309746	−	0.309746i
$540$	−5.00417e7	+	2.34226e7i	−0.317798	+	0.148749i
$541$	−1.27351e8	−	1.27351e8i	−0.804285	−	0.804285i	0.179478	−	0.983762i	$-0.442559\pi$
$541$	−1.27351e8	−	1.27351e8i	−0.804285	−	0.804285i	−0.983762	+	0.179478i	$0.942559\pi$
$542$	−2.03512e8	+	4.52712e7i	−1.27818	+	0.284331i
$543$			1.85007e7i			0.115555i
$544$	7.15698e7	+	3.69300e7i	0.444563	+	0.229394i
$545$	−6.23531e7			−0.385184
$546$	7.53620e6	+	3.38782e7i	0.0462993	+	0.208133i
$547$	−5.25427e6	+	5.25427e6i	−0.0321034	+	0.0321034i	−0.722976	−	0.690873i	$-0.757226\pi$
$547$	−5.25427e6	+	5.25427e6i	−0.0321034	+	0.0321034i	0.690873	+	0.722976i	$0.257226\pi$
$548$	1.29063e8	+	2.75739e8i	0.784259	+	1.67555i
$549$	6.92805e7	−	6.92805e7i	0.418691	−	0.418691i
$550$	−5.56837e7	−	3.54181e7i	−0.334688	−	0.212881i
$551$	1.54356e7			0.0922719
$552$	−1.06035e8	−	1.37269e7i	−0.630424	−	0.0816120i
$553$			2.39124e7i			0.141399i
$554$	−1.22290e8	−	7.77838e7i	−0.719221	−	0.457467i
$555$	−3.23495e7	−	3.23495e7i	−0.189229	−	0.189229i
$556$	−5.79070e7	−	2.09820e7i	−0.336905	−	0.122074i
$557$	−2.15757e7	−	2.15757e7i	−0.124853	−	0.124853i	0.641919	−	0.766772i	$-0.278138\pi$
$557$	−2.15757e7	−	2.15757e7i	−0.124853	−	0.124853i	−0.766772	+	0.641919i	$0.778138\pi$
$558$	4.98701e7	+	2.24185e8i	0.287037	+	1.29034i
$559$			4.05084e8i			2.31905i
$560$	−2.16476e6	−	2.39487e7i	−0.0123267	−	0.136370i
$561$	−1.95213e7			−0.110566
$562$	3.07888e8	−	6.84898e7i	1.73454	−	0.385849i
$563$	1.21939e8	−	1.21939e8i	0.683310	−	0.683310i	−0.277434	−	0.960745i	$-0.589484\pi$
$563$	1.21939e8	−	1.21939e8i	0.683310	−	0.683310i	0.960745	+	0.277434i	$0.0894841\pi$
$564$	2.87444e7	+	1.04153e7i	0.160220	+	0.0580541i
$565$	−3.15666e7	+	3.15666e7i	−0.175018	+	0.175018i
$566$	1.32572e7	−	2.08427e7i	0.0731141	−	0.114949i
$567$	2.46039e7			0.134976
$568$	7.01206e7	+	9.09754e7i	0.382649	+	0.496454i
$569$		−	8.97748e6i		−	0.0487324i	−0.999703	−	0.0243662i	$-0.992243\pi$
$569$		−	8.97748e6i		−	0.0487324i	0.999703	−	0.0243662i	$-0.00775677\pi$
$570$	6.31359e6	−	9.92611e6i	0.0340919	−	0.0535987i
$571$	8.45561e7	+	8.45561e7i	0.454189	+	0.454189i	0.896742	−	0.442553i	$-0.145927\pi$
$571$	8.45561e7	+	8.45561e7i	0.454189	+	0.454189i	−0.442553	+	0.896742i	$0.645927\pi$
$572$	−5.71976e7	−	1.22201e8i	−0.305626	−	0.652960i
$573$	5.82859e7	+	5.82859e7i	0.309813	+	0.309813i
$574$	7.75751e7	−	1.72566e7i	0.410191	−	0.0912472i
$575$		−	2.16886e8i		−	1.14085i
$576$	−1.46771e8	−	3.86484e7i	−0.768020	−	0.202238i
$577$	1.49638e8			0.778958			0.389479	−	0.921035i	$-0.372655\pi$
$577$	1.49638e8			0.778958			0.389479	+	0.921035i	$0.372655\pi$
$578$	−3.14369e7	−	1.41321e8i	−0.162801	−	0.731853i
$579$	−9.67304e6	+	9.67304e6i	−0.0498342	+	0.0498342i
$580$	2.16412e7	−	1.01294e7i	0.110917	−	0.0519160i
$581$	2.25649e7	−	2.25649e7i	0.115055	−	0.115055i
$582$	−1.20669e8	−	7.67528e7i	−0.612108	−	0.389337i
$583$	6.77338e7			0.341822
$584$	−6.98709e7	+	5.38540e7i	−0.350798	+	0.270383i
$585$		−	1.01431e8i		−	0.506645i
$586$	1.86053e7	+	1.18340e7i	0.0924578	+	0.0588086i
$587$	1.40444e8	+	1.40444e8i	0.694368	+	0.694368i	0.963190	−	0.268822i	$-0.0866343\pi$
$587$	1.40444e8	+	1.40444e8i	0.694368	+	0.694368i	−0.268822	+	0.963190i	$0.586634\pi$
$588$	−2.82487e7	+	7.79619e7i	−0.138953	+	0.383487i
$589$	−7.81130e7	−	7.81130e7i	−0.382276	−	0.382276i
$590$	−3.50312e7	−	1.57479e8i	−0.170568	−	0.766771i
$591$			1.55875e8i			0.755115i
$592$	−2.55583e7	−	2.82752e8i	−0.123188	−	1.36282i
$593$	−2.32854e8			−1.11666			−0.558329	−	0.829620i	$-0.688557\pi$
$593$	−2.32854e8			−1.11666			−0.558329	+	0.829620i	$0.688557\pi$
$594$	8.11276e7	−	1.80468e7i	0.387088	−	0.0861077i
$595$	1.02027e7	−	1.02027e7i	0.0484355	−	0.0484355i
$596$	−6.12649e6	+	1.69081e7i	−0.0289383	+	0.0798650i
$597$	1.17072e8	−	1.17072e8i	0.550214	−	0.550214i
$598$	2.37984e8	−	3.74154e8i	1.11287	−	1.74963i
$599$	2.24370e8			1.04396			0.521981	−	0.852957i	$-0.325193\pi$
$599$	2.24370e8			1.04396			0.521981	+	0.852957i	$0.325193\pi$
$600$	−1.02422e7	+	7.91177e7i	−0.0474178	+	0.366286i
$601$			4.21449e7i			0.194143i	0.995277	+	0.0970715i	$0.0309476\pi$
$601$			4.21449e7i			0.194143i	−0.995277	+	0.0970715i	$0.969052\pi$
$602$	5.82822e7	−	9.16303e7i	0.267145	−	0.420000i
$603$	1.05633e8	+	1.05633e8i	0.481780	+	0.481780i
$604$	−2.11623e8	+	9.90527e7i	−0.960400	+	0.449527i
$605$	5.14807e7	+	5.14807e7i	0.232476	+	0.232476i
$606$	5.32270e7	−	1.18404e7i	0.239174	−	0.0532043i
$607$			4.40611e7i			0.197011i	0.995137	+	0.0985053i	$0.0314061\pi$
$607$			4.40611e7i			0.197011i	−0.995137	+	0.0985053i	$0.968594\pi$
$608$	6.95448e7	−	2.22029e7i	0.309424	−	0.0987870i
$609$	9.24534e6			0.0409327
$610$	1.58412e7	+	7.12123e7i	0.0697908	+	0.313737i
$611$	−8.96579e7	+	8.96579e7i	−0.393066	+	0.393066i
$612$	−3.86069e7	−	8.24826e7i	−0.168427	−	0.359839i
$613$	−1.77366e8	+	1.77366e8i	−0.769996	+	0.769996i	−0.978106	−	0.208109i	$-0.933269\pi$
$613$	−1.77366e8	+	1.77366e8i	−0.769996	+	0.769996i	0.208109	+	0.978106i	$0.433269\pi$
$614$	1.76895e8	+	1.12516e8i	0.764207	+	0.486080i
$615$	6.01847e7			0.258738
$616$	−4.64376e6	+	3.58714e7i	−0.0198668	+	0.153464i
$617$		−	1.01618e8i		−	0.432628i	−0.976324	−	0.216314i	$-0.930596\pi$
$617$		−	1.01618e8i		−	0.432628i	0.976324	−	0.216314i	$-0.0694036\pi$
$618$	−1.06241e8	−	6.75754e7i	−0.450118	−	0.286301i
$619$	1.82774e8	+	1.82774e8i	0.770626	+	0.770626i	0.978216	−	0.207590i	$-0.0665620\pi$
$619$	1.82774e8	+	1.82774e8i	0.770626	+	0.770626i	−0.207590	+	0.978216i	$0.566562\pi$
$620$	−1.60777e8	−	5.82561e7i	−0.674605	−	0.244437i
$621$	1.93140e8	+	1.93140e8i	0.806488	+	0.806488i
$622$	1.41027e7	+	6.33973e7i	0.0586047	+	0.263451i
$623$		−	5.04851e7i		−	0.208785i
$624$	−1.04483e8	+	1.25249e8i	−0.430023	+	0.515490i
$625$	−1.16456e8			−0.477005
$626$	−9.69292e7	+	2.15619e7i	−0.395122	+	0.0878951i
$627$	−1.25125e7	+	1.25125e7i	−0.0507623	+	0.0507623i
$628$	1.48180e8	+	5.36916e7i	0.598289	+	0.216784i
$629$	1.20459e8	−	1.20459e8i	0.484045	−	0.484045i
$630$	−1.45936e7	+	2.29438e7i	−0.0583634	+	0.0917580i
$631$	−4.68747e8			−1.86574			−0.932869	−	0.360217i	$-0.882703\pi$
$631$	−4.68747e8			−1.86574			−0.932869	+	0.360217i	$0.882703\pi$
$632$	−8.90089e7	+	6.86049e7i	−0.352600	+	0.271772i
$633$			1.53924e8i			0.606870i
$634$	−1.14627e8	+	1.80214e8i	−0.449799	+	0.707166i
$635$	1.15353e7	+	1.15353e7i	0.0450514	+	0.0450514i
$636$	−3.47116e7	−	7.41602e7i	−0.134928	−	0.288270i
$637$	−2.43174e8	−	2.43174e8i	−0.940804	−	0.940804i
$638$	−3.50847e7	+	7.80460e6i	−0.135100	+	0.0300531i
$639$		−	1.29887e8i		−	0.497811i
$640$	8.29334e7	−	7.67670e7i	0.316366	−	0.292843i
$641$	−1.17901e8			−0.447653			−0.223827	−	0.974629i	$-0.571855\pi$
$641$	−1.17901e8			−0.447653			−0.223827	+	0.974629i	$0.571855\pi$
$642$	3.61225e7	+	1.62385e8i	0.136513	+	0.613678i
$643$	7.26292e7	−	7.26292e7i	0.273198	−	0.273198i	−0.557188	−	0.830386i	$-0.688120\pi$
$643$	7.26292e7	−	7.26292e7i	0.273198	−	0.273198i	0.830386	+	0.557188i	$0.188120\pi$
$644$	−1.07664e8	+	5.03936e7i	−0.403101	+	0.188676i
$645$	5.81529e7	−	5.81529e7i	0.216717	−	0.216717i
$646$	3.69615e7	+	2.35097e7i	0.137105	+	0.0872066i
$647$	−1.71222e8			−0.632190			−0.316095	−	0.948728i	$-0.602372\pi$
$647$	−1.71222e8			−0.632190			−0.316095	+	0.948728i	$0.602372\pi$
$648$	7.05890e7	+	9.15831e7i	0.259425	+	0.336581i
$649$			2.42671e8i			0.887736i
$650$	−2.79173e8	−	1.77571e8i	−1.01656	−	0.646593i
$651$	−4.67866e7	−	4.67866e7i	−0.169582	−	0.169582i
$652$	−3.31951e7	+	9.16131e7i	−0.119765	+	0.330533i
$653$	−2.24233e8	−	2.24233e8i	−0.805305	−	0.805305i	0.178614	−	0.983919i	$-0.442839\pi$
$653$	−2.24233e8	−	2.24233e8i	−0.805305	−	0.805305i	−0.983919	+	0.178614i	$0.942839\pi$
$654$	−2.46203e7	−	1.10678e8i	−0.0880156	−	0.395664i
$655$		−	9.23226e7i		−	0.328537i
$656$	2.86798e8	+	2.39248e8i	1.01593	+	0.847494i
$657$	9.97560e7			0.351757
$658$	3.31804e7	−	7.38099e6i	0.116467	−	0.0259082i
$659$	1.41194e8	−	1.41194e8i	0.493354	−	0.493354i	−0.416007	−	0.909361i	$-0.636571\pi$
$659$	1.41194e8	−	1.41194e8i	0.493354	−	0.493354i	0.909361	+	0.416007i	$0.136571\pi$
$660$	−9.33173e6	+	2.57541e7i	−0.0324586	+	0.0895806i
$661$	1.20007e8	−	1.20007e8i	0.415531	−	0.415531i	−0.468129	−	0.883660i	$-0.655072\pi$
$661$	1.20007e8	−	1.20007e8i	0.415531	−	0.415531i	0.883660	+	0.468129i	$0.155072\pi$
$662$	1.58177e8	−	2.48683e8i	0.545217	−	0.857181i
$663$	−9.78710e7			−0.335825
$664$	1.48732e8	+	1.92542e7i	0.508043	+	0.0657691i
$665$		−	1.30792e7i		−	0.0444749i
$666$	−1.72300e8	+	2.70887e8i	−0.583261	+	0.916993i
$667$	−8.35261e7	−	8.35261e7i	−0.281478	−	0.281478i
$668$	2.74447e8	−	1.28458e8i	0.920722	−	0.430955i
$669$	3.89251e7	+	3.89251e7i	0.130002	+	0.130002i
$670$	−1.08579e8	+	2.41533e7i	−0.361011	+	0.0803069i
$671$		−	1.09736e8i		−	0.363231i
$672$	4.16546e7	−	1.32987e7i	0.137263	−	0.0438229i
$673$	−3.11213e8			−1.02097			−0.510484	−	0.859887i	$-0.670534\pi$
$673$	−3.11213e8			−1.02097			−0.510484	+	0.859887i	$0.670534\pi$
$674$	1.05011e8	+	4.72065e8i	0.342969	+	1.54178i
$675$	1.44111e8	−	1.44111e8i	0.468581	−	0.468581i
$676$	−1.55807e8	−	3.32876e8i	−0.504366	−	1.07756i
$677$	2.14919e8	−	2.14919e8i	0.692644	−	0.692644i	−0.270169	−	0.962813i	$-0.587080\pi$
$677$	2.14919e8	−	2.14919e8i	0.692644	−	0.692644i	0.962813	+	0.270169i	$0.0870797\pi$
$678$	−6.84953e7	−	4.35670e7i	−0.219772	−	0.139788i
$679$	−1.59000e8			−0.507912
$680$	6.72491e7	+	8.70577e6i	0.213875	+	0.0276873i
$681$		−	1.97294e8i		−	0.624702i
$682$	2.17044e8	+	1.38053e8i	0.684219	+	0.435203i
$683$	−95642.2	−	95642.2i	−0.000300184	−	0.000300184i	0.706957	−	0.707257i	$-0.250068\pi$
$683$	−95642.2	−	95642.2i	−0.000300184	−	0.000300184i	−0.707257	+	0.706957i	$0.750068\pi$
$684$	−7.76144e7	−	2.81228e7i	−0.242535	−	0.0878801i
$685$	1.81261e8	+	1.81261e8i	0.563939	+	0.563939i
$686$	4.22843e7	+	1.90084e8i	0.130980	+	0.588808i
$687$		−	1.49273e8i		−	0.460375i
$688$	5.08288e8	−	4.59448e7i	1.56079	−	0.141082i
$689$	3.39587e8			1.03823
$690$	−8.78771e7	+	1.95483e7i	−0.267503	+	0.0595061i
$691$	−3.07156e8	+	3.07156e8i	−0.930946	+	0.930946i	−0.997765	−	0.0668189i	$-0.978715\pi$
$691$	−3.07156e8	+	3.07156e8i	−0.930946	+	0.930946i	0.0668189	+	0.997765i	$0.478715\pi$
$692$	−1.89618e8	−	6.87064e7i	−0.572219	−	0.207338i
$693$	2.89221e7	−	2.89221e7i	0.0869022	−	0.0869022i
$694$	−1.93565e8	+	3.04319e8i	−0.579093	+	0.910439i
$695$	−5.18589e7			−0.154479
$696$	2.65250e7	+	3.44139e7i	0.0786733	+	0.102072i
$697$			2.24108e8i			0.661848i
$698$	−7.84566e6	+	1.23348e7i	−0.0230708	+	0.0362715i
$699$	5.14804e7	+	5.14804e7i	0.150734	+	0.150734i
$700$	3.76009e7	+	8.03332e7i	0.109624	+	0.234208i
$701$	2.30522e8	+	2.30522e8i	0.669205	+	0.669205i	0.957532	−	0.288327i	$-0.0930990\pi$
$701$	2.30522e8	+	2.30522e8i	0.669205	+	0.669205i	−0.288327	+	0.957532i	$0.593099\pi$
$702$	4.06737e8	−	9.04788e7i	1.17572	−	0.261538i
$703$		−	1.54420e8i		−	0.444465i
$704$	−1.46847e8	+	8.56300e7i	−0.420869	+	0.245419i
$705$	2.57422e7			0.0734646
$706$	−5.71505e7	−	2.56914e8i	−0.162408	−	0.730085i
$707$	4.28681e7	−	4.28681e7i	0.121304	−	0.121304i
$708$	2.65695e8	−	1.24362e8i	0.748659	−	0.350419i
$709$	1.34580e8	−	1.34580e8i	0.377607	−	0.377607i	−0.492631	−	0.870238i	$-0.663965\pi$
$709$	1.34580e8	−	1.34580e8i	0.377607	−	0.377607i	0.870238	+	0.492631i	$0.163965\pi$
$710$	8.16041e7	+	5.19050e7i	0.228001	+	0.145022i
$711$	1.27080e8			0.353564
$712$	1.87920e8	−	1.44842e8i	0.520635	−	0.401287i
$713$			8.45378e8i			2.33229i
$714$	2.21385e7	+	1.40814e7i	0.0608210	+	0.0386857i
$715$	−8.03306e7	−	8.03306e7i	−0.219767	−	0.219767i
$716$	1.12724e8	−	3.11099e8i	0.307098	−	0.847539i
$717$	−1.72755e8	−	1.72755e8i	−0.468677	−	0.468677i
$718$	−1.17680e8	−	5.29019e8i	−0.317930	−	1.42922i
$719$		−	4.27779e8i		−	1.15089i	−0.817841	−	0.575444i	$-0.804829\pi$
$719$		−	4.27779e8i		−	1.15089i	0.817841	−	0.575444i	$-0.195171\pi$
$720$	−1.27273e8	+	1.15044e7i	−0.340987	+	0.0308223i
$721$	−1.39989e8			−0.373497
$722$	−3.28627e8	+	7.31031e7i	−0.873155	+	0.194234i
$723$	1.87225e7	−	1.87225e7i	0.0495392	−	0.0495392i
$724$	−3.29316e7	+	9.08857e7i	−0.0867754	+	0.239486i
$725$	−6.23226e7	+	6.23226e7i	−0.163543	+	0.163543i
$726$	−7.10519e7	+	1.11706e8i	−0.185680	+	0.291923i
$727$	−2.21795e8			−0.577228			−0.288614	−	0.957445i	$-0.593194\pi$
$727$	−2.21795e8			−0.577228			−0.288614	+	0.957445i	$0.593194\pi$
$728$	−2.32817e7	+	1.79843e8i	−0.0603421	+	0.466122i
$729$			1.22979e7i			0.0317429i
$730$	−3.98640e7	+	6.26735e7i	−0.102474	+	0.161107i
$731$	2.16542e8	+	2.16542e8i	0.554358	+	0.554358i
$732$	−1.20148e8	+	5.62367e7i	−0.306326	+	0.143379i
$733$	1.50134e8	+	1.50134e8i	0.381213	+	0.381213i	0.871539	−	0.490326i	$-0.163122\pi$
$733$	1.50134e8	+	1.50134e8i	0.381213	+	0.381213i	−0.490326	+	0.871539i	$0.663122\pi$
$734$	−5.65287e8	+	1.25748e8i	−1.42949	+	0.317990i
$735$			6.98191e7i			0.175838i
$736$	−4.96470e8	−	2.56179e8i	−1.24526	−	0.642554i
$737$	1.67317e8			0.417963
$738$	−9.17083e7	−	4.12265e8i	−0.228160	−	1.02567i
$739$	5.75281e7	−	5.75281e7i	0.142543	−	0.142543i	−0.632234	−	0.774777i	$-0.717862\pi$
$739$	5.75281e7	−	5.75281e7i	0.142543	−	0.142543i	0.774777	+	0.632234i	$0.217862\pi$
$740$	−1.01336e8	−	2.16501e8i	−0.250074	−	0.534276i
$741$	−6.27320e7	+	6.27320e7i	−0.154182	+	0.154182i
$742$	−7.68148e7	−	4.88587e7i	−0.188033	−	0.119600i
$743$	−1.07863e8			−0.262969			−0.131484	−	0.991318i	$-0.541974\pi$
$743$	−1.07863e8			−0.262969			−0.131484	+	0.991318i	$0.541974\pi$
$744$	3.99222e7	−	3.08385e8i	0.0969383	−	0.748815i
$745$			1.51421e7i			0.0366200i
$746$	3.05718e8	+	1.94455e8i	0.736384	+	0.468383i
$747$	−1.19919e8	−	1.19919e8i	−0.287690	−	0.287690i
$748$	−9.58995e7	−	3.47482e7i	−0.229146	−	0.0830287i
$749$	1.30782e8	+	1.30782e8i	0.311245	+	0.311245i
$750$	3.25012e7	+	1.46105e8i	0.0770398	+	0.346324i
$751$		−	5.38301e7i		−	0.127088i	−0.997979	−	0.0635441i	$-0.979760\pi$
$751$		−	5.38301e7i		−	0.127088i	0.997979	−	0.0635441i	$-0.0202404\pi$
$752$	1.22669e8	+	1.02331e8i	0.288458	+	0.240633i
$753$	−2.01583e8			−0.472138
$754$	−1.75899e8	+	3.91288e7i	−0.410345	+	0.0912814i
$755$	−1.39113e8	+	1.39113e8i	−0.323242	+	0.323242i
$756$	−1.05022e8	−	3.80538e7i	−0.243061	−	0.0880709i
$757$	−7.62579e7	+	7.62579e7i	−0.175791	+	0.175791i	−0.789518	−	0.613727i	$-0.789670\pi$
$757$	−7.62579e7	+	7.62579e7i	−0.175791	+	0.175791i	0.613727	+	0.789518i	$0.289670\pi$
$758$	−1.18829e8	+	1.86820e8i	−0.272844	+	0.428960i
$759$	1.35417e8			0.309704
$760$	4.86845e7	−	3.75243e7i	0.110905	−	0.0854815i
$761$		−	4.12448e8i		−	0.935870i	−0.883763	−	0.467935i	$-0.844998\pi$
$761$		−	4.12448e8i		−	0.935870i	0.883763	−	0.467935i	$-0.155002\pi$
$762$	−1.59206e7	+	2.50301e7i	−0.0359828	+	0.0565715i
$763$	−8.91379e7	−	8.91379e7i	−0.200673	−	0.200673i
$764$	1.82583e8	+	3.90083e8i	0.409430	+	0.874735i
$765$	−5.42211e7	−	5.42211e7i	−0.121111	−	0.121111i
$766$	7.26061e8	−	1.61512e8i	1.61542	−	0.359352i
$767$			1.21664e9i			2.69635i
$768$	1.69009e8	+	1.16897e8i	0.373101	+	0.258058i
$769$	2.49452e8			0.548539			0.274270	−	0.961653i	$-0.411564\pi$
$769$	2.49452e8			0.548539			0.274270	+	0.961653i	$0.411564\pi$
$770$	6.61312e6	+	2.97286e7i	0.0144855	+	0.0651181i
$771$	−1.07861e8	+	1.07861e8i	−0.235342	+	0.235342i
$772$	−6.47376e7	+	3.03012e7i	−0.140703	+	0.0658579i
$773$	−2.20608e8	+	2.20608e8i	−0.477620	+	0.477620i	−0.904370	−	0.426750i	$-0.859659\pi$
$773$	−2.20608e8	+	2.20608e8i	−0.477620	+	0.477620i	0.426750	+	0.904370i	$0.359659\pi$
$774$	−4.86960e8	−	3.09735e8i	−1.05020	−	0.667986i
$775$	6.30775e8			1.35509
$776$	−4.56174e8	−	5.91846e8i	−0.976215	−	1.26655i
$777$		−	9.24915e7i		−	0.197169i
$778$	1.08127e8	+	6.87749e7i	0.229612	+	0.146046i
$779$	1.43645e8	+	1.43645e8i	0.303864	+	0.303864i
$780$	−4.67851e7	+	1.29119e8i	−0.0985880	+	0.272087i
$781$	−1.02867e8	−	1.02867e8i	−0.215935	−	0.215935i
$782$	−7.27913e7	−	3.27225e8i	−0.152216	−	0.684268i
$783$		−	1.10998e8i		−	0.231223i
$784$	−2.77547e8	+	3.32709e8i	−0.575955	+	0.690425i
$785$	1.32703e8			0.274330
$786$	1.63874e8	−	3.64538e7i	0.337476	−	0.0750716i
$787$	1.77205e8	−	1.77205e8i	0.363540	−	0.363540i	−0.501574	−	0.865115i	$-0.667246\pi$
$787$	1.77205e8	−	1.77205e8i	0.363540	−	0.363540i	0.865115	+	0.501574i	$0.167246\pi$
$788$	−2.77460e8	+	7.65743e8i	−0.567050	+	1.56496i
$789$	−1.77665e8	+	1.77665e8i	−0.361718	+	0.361718i
$790$	−5.07830e7	+	7.98402e7i	−0.103000	+	0.161935i
$791$	−9.02531e7			−0.182361
$792$	1.90635e8	+	2.46787e7i	0.383731	+	0.0496761i
$793$		−	5.50169e8i		−	1.10326i
$794$	4.59946e8	−	7.23118e8i	0.918851	−	1.44460i
$795$	−4.87503e7	−	4.87503e7i	−0.0970232	−	0.0970232i
$796$	7.83516e8	−	3.66734e8i	1.55349	−	0.727130i
$797$	−1.35567e8	−	1.35567e8i	−0.267780	−	0.267780i	0.560425	−	0.828205i	$-0.310638\pi$
$797$	−1.35567e8	−	1.35567e8i	−0.267780	−	0.267780i	−0.828205	+	0.560425i	$0.810638\pi$
$798$	2.32157e7	−	5.16435e6i	0.0456850	−	0.0101626i
$799$			9.58553e7i			0.187921i
$800$	−1.91147e8	+	3.70439e8i	−0.373333	+	0.723514i
$801$	−2.68298e8			−0.522058
$802$	−1.06058e8	−	4.76774e8i	−0.205600	−	0.924250i
$803$	7.90039e7	−	7.90039e7i	0.152582	−	0.152582i
$804$	−8.57451e7	−	1.83192e8i	−0.164984	−	0.352483i
$805$	−7.07747e7	+	7.07747e7i	−0.135672	+	0.135672i
$806$	1.08816e9	+	6.92135e8i	2.07820	+	1.32186i
$807$	8.84214e7			0.168243
$808$	2.82557e8	+	3.65786e7i	0.535638	+	0.0693415i
$809$		−	8.89106e8i		−	1.67922i	−0.543188	−	0.839611i	$-0.682783\pi$
$809$		−	8.89106e8i		−	1.67922i	0.543188	−	0.839611i	$-0.317217\pi$
$810$	8.21491e7	+	5.22517e7i	0.154578	+	0.0983207i
$811$	1.46332e8	+	1.46332e8i	0.274331	+	0.274331i	0.830841	−	0.556510i	$-0.187860\pi$
$811$	1.46332e8	+	1.46332e8i	0.274331	+	0.274331i	−0.556510	+	0.830841i	$0.687860\pi$
$812$	4.54183e7	+	1.64569e7i	0.0848325	+	0.0307382i
$813$	−2.25713e8	−	2.25713e8i	−0.420035	−	0.420035i
$814$	7.80782e7	+	3.50992e8i	0.144763	+	0.650765i
$815$			8.20445e7i			0.151557i
$816$	1.11006e7	+	1.22806e8i	0.0204303	+	0.226021i
$817$	2.77592e8			0.509028
$818$	−1.17967e8	+	2.62418e7i	−0.215527	+	0.0479440i
$819$	1.45003e8	−	1.45003e8i	0.263951	−	0.263951i
$820$	2.95661e8	+	1.07130e8i	0.536231	+	0.194298i
$821$	3.44798e8	−	3.44798e8i	0.623067	−	0.623067i	−0.323247	−	0.946315i	$-0.604775\pi$
$821$	3.44798e8	−	3.44798e8i	0.623067	−	0.623067i	0.946315	+	0.323247i	$0.104775\pi$
$822$	−2.50170e8	+	3.93312e8i	−0.450422	+	0.708145i
$823$	3.93148e8			0.705272			0.352636	−	0.935761i	$-0.385285\pi$
$823$	3.93148e8			0.705272			0.352636	+	0.935761i	$0.385285\pi$
$824$	−4.01629e8	−	5.21079e8i	−0.717866	−	0.931369i
$825$		−	1.01040e8i		−	0.179942i
$826$	1.75047e8	−	2.75206e8i	0.310609	−	0.488334i
$827$	−6.81653e8	−	6.81653e8i	−1.20517	−	1.20517i	−0.972575	−	0.232591i	$-0.925280\pi$
$827$	−6.81653e8	−	6.81653e8i	−1.20517	−	1.20517i	−0.232591	−	0.972575i	$-0.574720\pi$
$828$	2.67811e8	+	5.72171e8i	0.471778	+	1.00794i
$829$	−3.57125e7	−	3.57125e7i	−0.0626840	−	0.0626840i	0.675070	−	0.737754i	$-0.264113\pi$
$829$	−3.57125e7	−	3.57125e7i	−0.0626840	−	0.0626840i	−0.737754	+	0.675070i	$0.764113\pi$
$830$	1.23262e8	−	2.74198e7i	0.215574	−	0.0479545i
$831$		−	2.21901e8i		−	0.386684i
$832$	−7.36224e8	+	4.29311e8i	−1.27832	+	0.745421i
$833$	−2.59983e8			−0.449790
$834$	−2.04766e7	−	9.20504e7i	−0.0352988	−	0.158682i
$835$	1.80411e8	−	1.80411e8i	0.309888	−	0.309888i
$836$	−8.37409e7	+	3.91959e7i	−0.143324	+	0.0670845i
$837$	−5.61715e8	+	5.61715e8i	−0.957942	+	0.957942i
$838$	−4.75767e8	−	3.02616e8i	−0.808467	−	0.514232i
$839$	2.60869e8			0.441709			0.220854	−	0.975307i	$-0.429115\pi$
$839$	2.60869e8			0.441709			0.220854	+	0.975307i	$0.429115\pi$
$840$	2.91601e7	−	2.24756e7i	0.0491985	−	0.0379204i
$841$		−	5.46821e8i		−	0.919299i
$842$	8.20093e8	+	5.21627e8i	1.37381	+	0.873823i
$843$	3.41477e8	+	3.41477e8i	0.570005	+	0.570005i
$844$	−2.73988e8	+	7.56162e8i	−0.455726	+	1.25773i
$845$	−2.18821e8	−	2.18821e8i	−0.362676	−	0.362676i
$846$	−3.92255e7	−	1.76334e8i	−0.0647824	−	0.291222i
$847$			1.47190e8i			0.242231i
$848$	−3.85161e7	−	4.26104e8i	−0.0631619	−	0.698759i
$849$	3.78199e7			0.0618012
$850$	−2.44157e8	+	5.43129e7i	−0.397570	+	0.0884394i
$851$	−8.35605e8	+	8.35605e8i	−1.35585	+	1.35585i
$852$	−5.99106e7	+	1.65343e8i	−0.0968690	+	0.267343i
$853$	−5.28624e8	+	5.28624e8i	−0.851727	+	0.851727i	−0.990346	−	0.138619i	$-0.955734\pi$
$853$	−5.28624e8	+	5.28624e8i	−0.851727	+	0.851727i	0.138619	+	0.990346i	$0.455734\pi$
$854$	−7.91567e7	+	1.24449e8i	−0.127091	+	0.199810i
$855$	−6.95079e7			−0.111208
$856$	−1.11594e8	+	8.62024e8i	−0.177918	+	1.37435i
$857$			1.51301e8i			0.240380i	0.992751	+	0.120190i	$0.0383504\pi$
$857$			1.51301e8i			0.240380i	−0.992751	+	0.120190i	$0.961650\pi$
$858$	1.10869e8	−	1.74307e8i	0.175529	−	0.275964i
$859$	−7.45240e8	−	7.45240e8i	−1.17576	−	1.17576i	−0.980815	−	0.194940i	$-0.937549\pi$
$859$	−7.45240e8	−	7.45240e8i	−1.17576	−	1.17576i	−0.194940	−	0.980815i	$-0.562451\pi$
$860$	3.89193e8	−	1.82166e8i	0.611885	−	0.286400i
$861$	8.60380e7	+	8.60380e7i	0.134797	+	0.134797i
$862$	−4.06072e8	+	9.03307e7i	−0.633988	+	0.141031i
$863$			4.11220e8i			0.639797i	0.947452	+	0.319899i	$0.103649\pi$
$863$			4.11220e8i			0.639797i	−0.947452	+	0.319899i	$0.896351\pi$
$864$	−1.59663e8	−	5.00100e8i	−0.247549	−	0.775382i
$865$	−1.69814e8			−0.262376
$866$	4.26286e7	+	1.91632e8i	0.0656368	+	0.295063i
$867$	1.56738e8	−	1.56738e8i	0.240502	−	0.240502i
$868$	−1.46561e8	−	3.13123e8i	−0.224109	−	0.478802i
$869$	1.00644e8	−	1.00644e8i	0.153365	−	0.153365i
$870$	3.08689e7	+	1.96344e7i	0.0468774	+	0.0298168i
$871$	8.38853e8			1.26950
$872$	7.60598e7	−	5.87536e8i	0.114711	−	0.886104i
$873$			8.44991e8i			1.27002i
$874$	−2.56397e8	−	1.63084e8i	−0.384042	−	0.244273i
$875$	1.17671e8	+	1.17671e8i	0.175649	+	0.175649i
$876$	−1.26987e8	−	4.60125e7i	−0.188906	−	0.0684484i
$877$	3.94205e8	+	3.94205e8i	0.584418	+	0.584418i	0.936114	−	0.351696i	$-0.114395\pi$
$877$	3.94205e8	+	3.94205e8i	0.584418	+	0.584418i	−0.351696	+	0.936114i	$0.614395\pi$
$878$	−5.94045e7	−	2.67046e8i	−0.0877679	−	0.394551i
$879$			3.37601e7i			0.0497092i
$880$	−9.16854e7	+	1.09908e8i	−0.134540	+	0.161280i
$881$	2.83493e8			0.414587			0.207293	−	0.978279i	$-0.433535\pi$
$881$	2.83493e8			0.414587			0.207293	+	0.978279i	$0.433535\pi$
$882$	4.78260e8	−	1.06389e8i	0.697041	−	0.155057i
$883$	−3.61828e7	+	3.61828e7i	−0.0525557	+	0.0525557i	−0.732896	−	0.680340i	$-0.761832\pi$
$883$	−3.61828e7	+	3.61828e7i	−0.0525557	+	0.0525557i	0.680340	+	0.732896i	$0.261832\pi$
$884$	−4.80797e8	−	1.74212e8i	−0.695993	−	0.252186i
$885$	1.74659e8	−	1.74659e8i	0.251976	−	0.251976i
$886$	−3.83306e8	+	6.02627e8i	−0.551118	+	0.866458i
$887$	−9.00315e8			−1.29010			−0.645051	−	0.764140i	$-0.723164\pi$
$887$	−9.00315e8			−1.29010			−0.645051	+	0.764140i	$0.723164\pi$
$888$	3.44281e8	−	2.65359e8i	0.491670	−	0.378962i
$889$			3.29810e7i			0.0469417i
$890$	1.07216e8	−	1.68563e8i	0.152086	−	0.239107i
$891$	−1.03554e8	−	1.03554e8i	−0.146398	−	0.146398i
$892$	1.21934e8	+	2.60509e8i	0.171803	+	0.367053i
$893$	6.14400e7	+	6.14400e7i	0.0862774	+	0.0862774i
$894$	−2.68775e7	+	5.97891e6i	−0.0376164	+	0.00836777i
$895$		−	2.78606e8i		−	0.388617i
$896$	2.28303e8	+	8.81532e6i	0.317385	+	0.0122550i
$897$	6.78918e8			0.940676
$898$	−1.40389e8	−	6.31105e8i	−0.193868	−	0.871511i
$899$	2.42921e8	−	2.42921e8i	0.334338	−	0.334338i
$900$	4.26923e8	−	1.99826e8i	0.585628	−	0.274110i
$901$	1.81530e8	−	1.81530e8i	0.248184	−	0.248184i
$902$	−3.99132e8	−	2.53872e8i	−0.543873	−	0.345935i
$903$	1.66267e8			0.225810
$904$	−2.58937e8	−	3.35949e8i	−0.350501	−	0.454745i
$905$			8.13931e7i			0.109810i
$906$	−3.01858e8	−	1.91999e8i	−0.405899	−	0.258176i
$907$	7.10707e8	+	7.10707e8i	0.952508	+	0.952508i	0.998922	−	0.0464139i	$-0.0147793\pi$
$907$	7.10707e8	+	7.10707e8i	0.952508	+	0.952508i	−0.0464139	+	0.998922i	$0.514779\pi$
$908$	3.51187e8	−	9.69219e8i	0.469117	−	1.29469i
$909$	−2.27818e8	−	2.27818e8i	−0.303317	−	0.303317i
$910$	3.31552e7	+	1.49046e8i	0.0439975	+	0.197786i
$911$		−	1.94238e8i		−	0.256908i	−0.991715	−	0.128454i	$-0.958998\pi$
$911$		−	1.94238e8i		−	0.256908i	0.991715	−	0.128454i	$-0.0410015\pi$
$912$	8.58295e7	+	7.15993e7i	0.113149	+	0.0943896i
$913$	−1.89945e8			−0.249583
$914$	5.17529e7	−	1.15124e7i	0.0677792	−	0.0150775i
$915$	−7.89810e7	+	7.89810e7i	−0.103100	+	0.103100i
$916$	2.65709e8	−	7.33313e8i	0.345716	−	0.954120i
$917$	1.31981e8	−	1.31981e8i	0.171161	−	0.171161i
$918$	1.69059e8	−	2.65792e8i	0.218530	−	0.343569i
$919$	1.37332e8			0.176940			0.0884699	−	0.996079i	$-0.471802\pi$
$919$	1.37332e8			0.176940			0.0884699	+	0.996079i	$0.471802\pi$
$920$	−4.66498e8	−	6.03908e7i	−0.599082	−	0.0775546i
$921$			3.20984e8i			0.410870i
$922$	−6.63212e8	+	1.04269e9i	−0.846174	+	1.33034i
$923$	−5.15730e8	−	5.15730e8i	−0.655869	−	0.655869i
$924$	−5.01575e7	+	2.34768e7i	−0.0635799	+	0.0297593i
$925$	6.23483e8	+	6.23483e8i	0.787770	+	0.787770i
$926$	−2.16057e8	+	4.80620e7i	−0.272105	+	0.0605297i
$927$			7.43955e8i			0.933915i
$928$	6.90483e7	+	2.16275e8i	0.0863990	+	0.270622i
$929$	1.05077e9			1.31057			0.655284	−	0.755383i	$-0.272549\pi$
$929$	1.05077e9			1.31057			0.655284	+	0.755383i	$0.272549\pi$
$930$	−5.68528e7	−	2.55575e8i	−0.0706810	−	0.317739i
$931$	−1.66640e8	+	1.66640e8i	−0.206505	+	0.206505i
$932$	1.61265e8	+	3.44537e8i	0.199201	+	0.425586i
$933$	−7.03135e7	+	7.03135e7i	−0.0865752	+	0.0865752i
$934$	2.95200e8	+	1.87765e8i	0.362307	+	0.230448i
$935$	−8.58832e7			−0.105069
$936$	9.55757e8	+	1.23728e8i	1.16552	+	0.150883i
$937$			5.71742e8i			0.694995i	0.937681	+	0.347497i	$0.112968\pi$
$937$			5.71742e8i			0.694995i	−0.937681	+	0.347497i	$0.887032\pi$
$938$	−1.89749e8	−	1.20692e8i	−0.229917	−	0.146241i
$939$	−1.07504e8	−	1.07504e8i	−0.129845	−	0.129845i
$940$	1.26460e8	+	4.58216e7i	0.152254	+	0.0551679i
$941$	6.22677e8	+	6.22677e8i	0.747299	+	0.747299i	0.973971	−	0.226672i	$-0.0727846\pi$
$941$	6.22677e8	+	6.22677e8i	0.747299	+	0.747299i	−0.226672	+	0.973971i	$0.572785\pi$
$942$	5.23983e7	+	2.35551e8i	0.0626851	+	0.281794i
$943$		−	1.55460e9i		−	1.85389i
$944$	1.52661e9	−	1.37992e8i	1.81473	−	0.164036i
$945$	−9.40531e7			−0.111449
$946$	−6.30959e8	+	1.40357e8i	−0.745295	+	0.165791i
$947$	−1.40284e8	+	1.40284e8i	−0.165180	+	0.165180i	−0.784857	−	0.619677i	$-0.787264\pi$
$947$	−1.40284e8	+	1.40284e8i	−0.165180	+	0.165180i	0.619677	+	0.784857i	$0.287264\pi$
$948$	−1.61769e8	−	5.86156e7i	−0.189877	−	0.0687999i
$949$	3.96090e8	−	3.96090e8i	0.463442	−	0.463442i
$950$	−1.21684e8	+	1.91310e8i	−0.141926	+	0.223134i
$951$	−3.27006e8			−0.380202
$952$	8.36916e7	+	1.08583e8i	0.0969998	+	0.125849i
$953$		−	6.36507e7i		−	0.0735402i	−0.999324	−	0.0367701i	$-0.988293\pi$
$953$		−	6.36507e7i		−	0.0735402i	0.999324	−	0.0367701i	$-0.0117069\pi$
$954$	−2.59654e8	+	4.08224e8i	−0.299055	+	0.470169i
$955$	2.56426e8	+	2.56426e8i	0.294410	+	0.294410i
$956$	−5.41163e8	−	1.15618e9i	−0.619376	−	1.32328i
$957$	−3.89122e7	−	3.89122e7i	−0.0443967	−	0.0443967i
$958$	1.81227e8	−	4.03139e7i	0.206123	−	0.0458520i
$959$			5.18249e8i			0.587601i
$960$	1.67322e8	+	4.40598e7i	0.189120	+	0.0498000i
$961$	−1.57113e9			−1.77028
$962$	3.91449e8	+	1.75972e9i	0.439694	+	1.97659i
$963$	6.95027e8	−	6.95027e8i	0.778256	−	0.778256i
$964$	1.25302e8	−	5.86490e7i	0.139870	−	0.0654680i
$965$	−4.25562e7	+	4.25562e7i	−0.0473566	+	0.0473566i
$966$	−1.53572e8	−	9.76807e7i	−0.170365	−	0.108362i
$967$	−4.74753e8			−0.525036			−0.262518	−	0.964927i	$-0.584553\pi$
$967$	−4.74753e8			−0.525036			−0.262518	+	0.964927i	$0.584553\pi$
$968$	−5.47886e8	+	4.22291e8i	−0.604038	+	0.465571i
$969$			6.70682e7i			0.0737132i
$970$	−5.30881e8	−	3.37671e8i	−0.581677	−	0.369980i
$971$	−3.13770e8	−	3.13770e8i	−0.342731	−	0.342731i	0.514662	−	0.857393i	$-0.327917\pi$
$971$	−3.13770e8	−	3.13770e8i	−0.342731	−	0.342731i	−0.857393	+	0.514662i	$0.827917\pi$
$972$	−3.14947e8	+	8.69203e8i	−0.342957	+	0.946504i
$973$	−7.41357e7	−	7.41357e7i	−0.0804802	−	0.0804802i
$974$	−2.67776e8	−	1.20376e9i	−0.289797	−	1.30275i
$975$		−	5.06571e8i		−	0.546546i
$976$	−6.90337e8	+	6.24005e7i	−0.742526	+	0.0671179i
$977$	−2.20914e7			−0.0236886			−0.0118443	−	0.999930i	$-0.503770\pi$
$977$	−2.20914e7			−0.0236886			−0.0118443	+	0.999930i	$0.503770\pi$
$978$	−1.45630e8	+	3.23955e7i	−0.155681	+	0.0346312i
$979$	−2.12484e8	+	2.12484e8i	−0.226453	+	0.226453i
$980$	−1.24279e8	+	3.42990e8i	−0.132044	+	0.364421i
$981$	−4.73714e8	+	4.73714e8i	−0.501775	+	0.501775i
$982$	6.93436e8	−	1.09021e9i	0.732271	−	1.15126i
$983$	−1.49327e9			−1.57209			−0.786047	−	0.618167i	$-0.787875\pi$
$983$	−1.49327e9			−1.57209			−0.786047	+	0.618167i	$0.787875\pi$
$984$	−7.34147e7	+	5.67103e8i	−0.0770545	+	0.595219i
$985$			6.85765e8i			0.717574i
$986$	−7.31121e7	+	1.14946e8i	−0.0762708	+	0.119912i
$987$	3.68002e7	+	3.68002e7i	0.0382735	+	0.0382735i
$988$	−4.19839e8	+	1.96511e8i	−0.435323	+	0.203758i
$989$	−1.50212e9	−	1.50212e9i	−1.55280	−	1.55280i
$990$	1.57989e8	−	3.51447e7i	0.162825	−	0.0362205i
$991$		−	7.94166e8i		−	0.816001i	−0.912982	−	0.408000i	$-0.866226\pi$
$991$		−	7.94166e8i		−	0.816001i	0.912982	−	0.408000i	$-0.133774\pi$
$992$	7.45051e8	−	1.44390e9i	0.763222	−	1.47911i
$993$	4.51246e8			0.460857
$994$	4.24569e7	+	1.90860e8i	0.0432304	+	0.194337i
$995$	5.15056e8	−	5.15056e8i	0.522859	−	0.522859i
$996$	9.73410e7	+	2.07966e8i	0.0985185	+	0.210482i
$997$	1.09278e9	−	1.09278e9i	1.10268	−	1.10268i	0.108592	−	0.994086i	$-0.465366\pi$
$997$	1.09278e9	−	1.09278e9i	1.10268	−	1.10268i	0.994086	−	0.108592i	$-0.0346342\pi$
$998$	1.03507e9	+	6.58363e8i	1.04130	+	0.662329i
$999$	−1.11044e9			−1.11378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.3.7	✓	22
4.3	odd	2		64.7.f.a.47.7		22
8.3	odd	2		128.7.f.a.95.5		22
8.5	even	2		128.7.f.b.95.7		22
16.3	odd	4		128.7.f.b.31.7		22
16.5	even	4		64.7.f.a.15.7		22
16.11	odd	4	inner	16.7.f.a.11.7	yes	22
16.13	even	4		128.7.f.a.31.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.7	✓	22	1.1	even	1	trivial
16.7.f.a.11.7	yes	22	16.11	odd	4	inner
64.7.f.a.15.7		22	16.5	even	4
64.7.f.a.47.7		22	4.3	odd	2
128.7.f.a.31.5		22	16.13	even	4
128.7.f.a.95.5		22	8.3	odd	2
128.7.f.b.31.7		22	16.3	odd	4
128.7.f.b.95.7		22	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73714 + 7.80912i) q^{2} +(-8.66104 + 8.66104i) q^{3} +(-57.9647 + 27.1311i) q^{4} +(-38.1039 + 38.1039i) q^{5} +(-82.6805 - 52.5897i) q^{6} -108.944 q^{7} +(-312.563 - 405.523i) q^{8} +578.973i q^{9} +O(q^{10})\)	\(q+(1.73714 + 7.80912i) q^{2} +(-8.66104 + 8.66104i) q^{3} +(-57.9647 + 27.1311i) q^{4} +(-38.1039 + 38.1039i) q^{5} +(-82.6805 - 52.5897i) q^{6} -108.944 q^{7} +(-312.563 - 405.523i) q^{8} +578.973i q^{9} +(-363.750 - 231.366i) q^{10} +(458.530 + 458.530i) q^{11} +(267.051 - 737.018i) q^{12} +(2298.86 + 2298.86i) q^{13} +(-189.251 - 850.759i) q^{14} -660.039i q^{15} +(2623.81 - 3145.29i) q^{16} +2457.77 q^{17} +(-4521.27 + 1005.76i) q^{18} +(1575.35 - 1575.35i) q^{19} +(1174.88 - 3242.48i) q^{20} +(943.571 - 943.571i) q^{21} +(-2784.18 + 4377.25i) q^{22} -17049.2 q^{23} +(6219.37 + 805.132i) q^{24} +12721.2i q^{25} +(-13958.7 + 21945.5i) q^{26} +(-11328.4 - 11328.4i) q^{27} +(6314.92 - 2955.77i) q^{28} +(4899.12 + 4899.12i) q^{29} +(5154.33 - 1146.58i) q^{30} -49584.6i q^{31} +(29119.9 + 15025.8i) q^{32} -7942.69 q^{33} +(4269.48 + 19193.0i) q^{34} +(4151.20 - 4151.20i) q^{35} +(-15708.1 - 33560.0i) q^{36} +(49011.4 - 49011.4i) q^{37} +(15038.7 + 9565.47i) q^{38} -39821.1 q^{39} +(27361.9 + 3542.15i) q^{40} +91183.4i q^{41} +(9007.57 + 5729.34i) q^{42} +(88105.2 + 88105.2i) q^{43} +(-39019.0 - 14138.1i) q^{44} +(-22061.1 - 22061.1i) q^{45} +(-29616.8 - 133139. i) q^{46} +39001.0i q^{47} +(4516.53 + 49966.4i) q^{48} -105780. q^{49} +(-99341.2 + 22098.5i) q^{50} +(-21286.8 + 21286.8i) q^{51} +(-195624. - 70882.3i) q^{52} +(73859.7 - 73859.7i) q^{53} +(68785.8 - 108144. i) q^{54} -34943.6 q^{55} +(34051.9 + 44179.4i) q^{56} +27288.3i q^{57} +(-29747.4 + 46768.3i) q^{58} +(264618. + 264618. i) q^{59} +(17907.6 + 38259.0i) q^{60} +(-119661. - 119661. i) q^{61} +(387212. - 86135.4i) q^{62} -63075.8i q^{63} +(-66753.4 + 253502. i) q^{64} -175191. q^{65} +(-13797.6 - 62025.5i) q^{66} +(182449. - 182449. i) q^{67} +(-142464. + 66681.8i) q^{68} +(147664. - 147664. i) q^{69} +(39628.5 + 25206.0i) q^{70} -224341. q^{71} +(234787. - 180965. i) q^{72} -172298. i q^{73} +(467876. + 297596. i) q^{74} +(-110179. - 110179. i) q^{75} +(-48573.6 + 134055. i) q^{76} +(-49954.2 - 49954.2i) q^{77} +(-69174.8 - 310968. i) q^{78} -219492. i q^{79} +(19870.3 + 219825. i) q^{80} -225840. q^{81} +(-712062. + 158398. i) q^{82} +(-207123. + 207123. i) q^{83} +(-29093.7 + 80293.9i) q^{84} +(-93650.5 + 93650.5i) q^{85} +(-534973. + 841075. i) q^{86} -84863.0 q^{87} +(42625.1 - 329264. i) q^{88} +463403. i q^{89} +(133955. - 210601. i) q^{90} +(-250448. - 250448. i) q^{91} +(988251. - 462563. i) q^{92} +(429454. + 429454. i) q^{93} +(-304563. + 67750.2i) q^{94} +120054. i q^{95} +(-382348. + 122069. i) q^{96} +1.45947e6 q^{97} +(-183755. - 826050. i) q^{98} +(-265476. + 265476. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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